// Numbas version: finer_feedback_settings
{"name": "INU0111/0511 S2 EXAM", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 5400, "percentPass": "50", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "S2 EXAM  box plot", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Elena is trying to draw a box plot. Answer the questions below to help her.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which average should she show?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["the&nbsp;median", "the mean", "the mode", "all of them"], "matrix": ["2", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How does she calculate the upper quartile?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["the difference between the highest and lowest values", "add up all of the numbers and divide by the number of numbers", "the difference between the quartiles", "the middle of the upper half of the data set"], "matrix": ["0", 0, "0", "2"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Averages freq table", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Use the frequency table below to calculate the averages</p>\n<table border=\"0.1\" style=\"border: solid;\">\n<tbody>\n<tr>\n<td>Class</td>\n<td>0</td>\n<td>1</td>\n<td>2</td>\n<td>3</td>\n<td>4</td>\n<td>5</td>\n</tr>\n<tr>\n<td>Frequency</td>\n<td>{f1}</td>\n<td>{f2}</td>\n<td>{f3}</td>\n<td>{f4}</td>\n<td>{f5}</td>\n<td>{f6}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>See \"show steps\" within this question for more help.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"f1": {"name": "f1", "group": "Frequencies", "definition": "random(5..20)", "description": "", "templateType": "anything", "can_override": false}, "f2": {"name": "f2", "group": "Frequencies", "definition": "f1+a", "description": "", "templateType": "anything", "can_override": false}, "f3": {"name": "f3", "group": "Frequencies", "definition": "f1-1", "description": "", "templateType": "anything", "can_override": false}, "f4": {"name": "f4", "group": "Frequencies", "definition": "f1-a", "description": "", "templateType": "anything", "can_override": false}, "f5": {"name": "f5", "group": "Frequencies", "definition": "f1-b", "description": "", "templateType": "anything", "can_override": false}, "f6": {"name": "f6", "group": "Frequencies", "definition": "a", "description": "", "templateType": "anything", "can_override": false}, "mp5": {"name": "mp5", "group": "Median calculations", "definition": "tot/2", "description": "", "templateType": "anything", "can_override": false}, "tot": {"name": "tot", "group": "Cumulative", "definition": "cf5+f6", "description": "", "templateType": "anything", "can_override": false}, "sfx": {"name": "sfx", "group": "Mean calculations", "definition": "0*f1+1*f2+2*f3+3*f4+4*f5+5*f6", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Median calculations", "definition": "switch(f1<mp5,1,f1=mp5,0.5,f1>mp5,0)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Median calculations", "definition": "switch(cf3<mp5,1,cf3=mp5,0.5,cf3>mp5,0)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Median calculations", "definition": "switch(cf2<mp5,1,cf2=mp5,0.5,cf2>mp5,0)", "description": "", "templateType": "anything", "can_override": false}, "a5": {"name": "a5", "group": "Median calculations", "definition": "switch(cf5<mp5,1,cf5=mp5,0.5,cf5>mp5,0)", "description": "", "templateType": "anything", "can_override": false}, "a4": {"name": "a4", "group": "Median calculations", "definition": "switch(cf4<mp5,1,cf4=mp5,0.5,cf4>mp5,0)", "description": "", "templateType": "anything", "can_override": false}, "cf4": {"name": "cf4", "group": "Cumulative", "definition": "cf3+f4", "description": "", "templateType": "anything", "can_override": false}, "cf5": {"name": "cf5", "group": "Cumulative", "definition": "cf4+f5", "description": "", "templateType": "anything", "can_override": false}, "cf2": {"name": "cf2", "group": "Cumulative", "definition": "f1+f2", "description": "", "templateType": "anything", "can_override": false}, "cf3": {"name": "cf3", "group": "Cumulative", "definition": "cf2+f3", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..f1-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(a..f1)", "description": "", "templateType": "anything", "can_override": false}, "mn": {"name": "mn", "group": "Mean calculations", "definition": "sfx/tot", "description": "", "templateType": "anything", "can_override": false}, "median": {"name": "median", "group": "Median calculations", "definition": "a1+a2+a3+a4+a5", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [{"name": "Frequencies", "variables": ["f1", "f2", "f3", "f4", "f5", "f6"]}, {"name": "Cumulative", "variables": ["cf2", "cf3", "cf4", "cf5", "tot"]}, {"name": "Median calculations", "variables": ["a1", "a2", "a3", "a4", "a5", "mp5", "median"]}, {"name": "Mean calculations", "variables": ["sfx", "mn"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the mean (correct to 2 decimal places)?</p>", "answer": "{mn}", "showPreview": false, "checkingType": "dp", "checkingAccuracy": "2", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the median?</p>", "minValue": "{median}", "maxValue": "{median}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the mode? <em>(If there is no mode, enter \"0\".)</em></p>", "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Bar Chart", "extensions": [], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "<p>The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.</p>", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates to <code>true</code> or <code>false</code>.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A bar chart shows discrete data</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "yes-no", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_answer_expr": "true"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Binomial Distribution 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Please give your answer to at least 3 decimal places.</strong></p>\n<p>It is estimated that $\\var{p_perc}$% of all Oldcastle University students read the student newspaper. A random sample of $\\var{n}$ students is chosen.</p>\n<p>Hint: for this question use the binomial distribution.</p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pr3": {"name": "pr3", "group": "Ungrouped variables", "definition": "((n*(n-1)*(n-2))/6)*(p^3)*(q^(n-3))", "description": "<p>probability that r = 3</p>", "templateType": "anything", "can_override": false}, "r0": {"name": "r0", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "answer1": {"name": "answer1", "group": "Ungrouped variables", "definition": "if(r=2,pr0+pr1, pr0+pr1+pr2)", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(0.1..0.2#0.05)", "description": "<p>the probability that an individual student cycles to college</p>", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "3", "description": "<p>more than r of the students cycle to college</p>", "templateType": "anything", "can_override": false}, "pr1": {"name": "pr1", "group": "Ungrouped variables", "definition": "n*p*q^(n-1)", "description": "<p>probability that r = 1</p>", "templateType": "anything", "can_override": false}, "pr2": {"name": "pr2", "group": "Ungrouped variables", "definition": "((n*(n-1))/2)*(p^2)*q^(n-2)", "description": "<p>probability that r = 2</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(6..12)", "description": "<p>sample size</p>", "templateType": "anything", "can_override": false}, "pr0": {"name": "pr0", "group": "Ungrouped variables", "definition": "q^n", "description": "<p>probability that&nbsp;r = 0</p>", "templateType": "anything", "can_override": false}, "qn": {"name": "qn", "group": "Ungrouped variables", "definition": "q^n", "description": "", "templateType": "anything", "can_override": false}, "answer2": {"name": "answer2", "group": "Ungrouped variables", "definition": "1-answer1", "description": "", "templateType": "anything", "can_override": false}, "p_perc": {"name": "p_perc", "group": "Ungrouped variables", "definition": "p*100", "description": "<p>percentage of students that cycle to college</p>", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "n-2", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "1-p", "description": "<p>probability tha an individual does not cycle to college</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p", "p_perc", "n", "q", "r", "pr0", "pr1", "pr2", "pr3", "answer1", "answer2", "qn", "r0", "n2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the probability that none of the Oldcastle <span>$\\var{n}$</span> students read the student newspaper.</p>", "minValue": "(q^n)-0.001", "maxValue": "(q^n)+0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the probability that at least&nbsp;$\\var{r}$ of the&nbsp;<span>$\\var{n}$</span> students read the student newspaper.</p>", "minValue": "answer2 -0.001", "maxValue": "answer2 +0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Correlation coeff 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Use the table below to calculate the correlation co-efficient for the relationship between science and maths grades for a group of students</p>\n<table width=\"876\" height=\"12\" border=\"1\" style=\"height: 12px;\">\n<tbody>\n<tr>\n<td style=\"width: 70.5556px;\">Science</td>\n<td style=\"width: 70.5556px;\">{x1}</td>\n<td style=\"width: 70.5556px;\">{x2}</td>\n<td style=\"width: 71.6667px;\">{x3}</td>\n<td style=\"width: 71.6667px;\">{x4}</td>\n<td style=\"width: 71.6667px;\">{x5}</td>\n<td style=\"width: 71.6667px;\">{x6}</td>\n<td style=\"width: 71.6667px;\">{x7}</td>\n<td style=\"width: 71.6667px;\">{x8}</td>\n<td style=\"width: 71.6667px;\">{x9}</td>\n</tr>\n<tr>\n<td style=\"width: 70.5556px;\">Maths</td>\n<td style=\"width: 70.5556px;\">{y1}</td>\n<td style=\"width: 70.5556px;\">{y2}</td>\n<td style=\"width: 71.6667px;\">{y3}</td>\n<td style=\"width: 71.6667px;\">{y4}</td>\n<td style=\"width: 71.6667px;\">{y5}</td>\n<td style=\"width: 71.6667px;\">{y6}</td>\n<td style=\"width: 71.6667px;\">{y7}</td>\n<td style=\"width: 71.6667px;\">{y8}</td>\n<td style=\"width: 71.6667px;\">{y9}</td>\n</tr>\n</tbody>\n</table>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "templateType": "anything", "can_override": false}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "templateType": "anything", "can_override": false}, "x6": {"name": "x6", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "templateType": "anything", "can_override": false}, "x7": {"name": "x7", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "x8": {"name": "x8", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "x9": {"name": "x9", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y4": {"name": "y4", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y5": {"name": "y5", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y7": {"name": "y7", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "y8": {"name": "y8", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "y9": {"name": "y9", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "sumxsq": {"name": "sumxsq", "group": "Ungrouped variables", "definition": "x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2+x9^2", "description": "", "templateType": "anything", "can_override": false}, "sumysq": {"name": "sumysq", "group": "Ungrouped variables", "definition": "y1^2+y2^2+y3^2+y4^2+y5^2+y6^2+y7^2+y8^2+y9^2", "description": "", "templateType": "anything", "can_override": false}, "sumxy": {"name": "sumxy", "group": "Ungrouped variables", "definition": "x1*y1+x2*y2+x3*y3+x4*y4+x5*y5+x6*y6+x7*y7+x8*y8+x9*y9", "description": "", "templateType": "anything", 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characteristic as the population", "When a sample is a targeted group", "A small group taken from a larger group", "The whole of the data"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Mean, median, mode", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}, {"name": "Paul Finley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2232/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "<div class=\"description\">\n<p>Topics covered are calculating the mean, median, mode and standard deviation.</p>\n<p>rebelmaths</p>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Calculate the mean, median and mode of the numbers in this list:</p>\n<p>$\\var{a2}, \\var{a7}, \\var{a1}, \\var{a5}, \\var{a3}, \\var{a6}$ and $\\var{a4}$.</p>", "advice": "<p>Mean: Add up all the numbers and divide by the number of numbers.</p>\n<p>Median: middle value</p>\n<p>Mode: most common value</p>\n<p></p>", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a7": {"name": "a7", "group": "Ungrouped variables", "definition": "random(131..140)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(116..121)", "description": "", "templateType": "anything", 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""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\text{mean}=\\;\\;$[[0]] (correct to two decimal places)</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{precround(1/7*(a1+a2+a3+a4+a5+a6+a7),2)}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.01, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 2, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a4}", "maxValue": "{a4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 2, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a2}", "maxValue": "{a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Poisson Distribution 1 doctors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Patricia Cogan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3359/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "<p>The number of patients arriving at a dentist&rsquo;s surgery each afternoon follows<br />a Poisson distribution, with a mean of four patients per hour.<br />Calculate the probability that in a particular one-hour period</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><span>T</span><span>he number of patients arriving at a doctor&rsquo;s surgery each afternoon follows a Poisson distribution, with a mean of $\\var{l}$ patients per hour<br/></span></p>\n<p></p>\n<p></p>\n<p><strong>Please give your answer to at least 3 decimal places.</strong></p>\n<p>Hint: for this question use the Poisson distribution</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(10..50#5)", "description": "<p>time interval</p>", "templateType": "anything", "can_override": false}, "answer1": {"name": "answer1", "group": "Ungrouped variables", "definition": "((e^-l)*(l^x))/x!", "description": "", "templateType": "anything", "can_override": false}, "prx": {"name": "prx", "group": "Ungrouped variables", "definition": "((e^-l)*(l^x))/x!", "description": "", "templateType": "anything", "can_override": false}, "answer2": {"name": "answer2", "group": "Ungrouped variables", "definition": "((e^-l)*(l^x))/x!+((e^-l)*(l^(x+1)))/(x+1)!+((e^-l)*(l^y))/y!", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "x+2", "description": "<p>upper value of X</p>", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random(1..5#1)", "description": "<p>time hour</p>", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(3..12)", "description": "<p>number of customers entering the shop</p>", "templateType": "anything", "can_override": false}, "prx1": {"name": "prx1", "group": "Ungrouped variables", "definition": "((e^-l)*(l^(x+1)))/(x+1)!", "description": "", "templateType": "anything", "can_override": false}, "pry": {"name": "pry", "group": "Ungrouped variables", "definition": "((e^-l)*(l^y))/y!", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(5..10#1)", "description": "<p>average, lambda</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["l", "x", "n", "y", "t", "answer1", "answer2", "prx", "prx1", "pry"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the mean?</p>\n<p>&nbsp;Mean = [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "l", "maxValue": "l", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span>Calculate the probability that in a particular one-hour period exactly $\\var{x}$ patients will arrive. Please give your answer to at least 3 decimal places.<br/><br/><br/></span></p>\n<p>$P(r = \\var{x}) =$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "answer1-0.005", "maxValue": "answer1+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "answer1-0.001", "maxValue": "answer1+0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span>Find the probability that in a particular one hour period, the number of patients who go into the waiting room</span><span> will be between $\\var{x}$ and $\\var{y}$ inclusive. Please give your answer to at least 3 decimal places.</span></p>\n<p><span>&nbsp;</span></p>\n<p>$P(\\var{x}\\leq r \\leq\\var{y}) =$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "answer2 -0.005", "maxValue": "answer2 +0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "answer2 -0.005", "maxValue": "answer2 +0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Prob from table1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The number of students in each year group of a school are shown in the table below.&nbsp;</p>\n<p></p>\n<table border=\"1\" cellpadding=\"1\" cellspacing=\"1\" style=\"float: left;\">\n<tbody>\n<tr>\n<td>Year</td>\n<td>5</td>\n<td>6</td>\n<td>7</td>\n<td>8</td>\n<td>9</td>\n</tr>\n<tr>\n<td>Number of students</td>\n<td>{Y5}</td>\n<td>{Y6}</td>\n<td>{Y7}</td>\n<td>{Y8}</td>\n<td>{Y9}</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"y5": {"name": "y5", "group": "Ungrouped variables", "definition": "random(35 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(35 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "y7": {"name": "y7", "group": "Ungrouped variables", "definition": "random(35 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "y8": {"name": "y8", "group": "Ungrouped variables", "definition": "random(35 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "y9": {"name": "y9", "group": "Ungrouped variables", "definition": "random(35 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "Y5+Y6+Y7+Y8+Y9", "description": "", "templateType": "anything", "can_override": false}, "PY9": {"name": "PY9", "group": "Ungrouped variables", "definition": "Y9/total", "description": "", "templateType": "anything", "can_override": false}, "PY8": {"name": "PY8", "group": "Ungrouped variables", "definition": "y8/total", "description": "", "templateType": "anything", "can_override": false}, "PY7": {"name": "PY7", "group": "Ungrouped variables", "definition": "y7/total", "description": "", "templateType": "anything", "can_override": false}, "py6": {"name": "py6", "group": "Ungrouped variables", "definition": "y6/total\n", "description": "", "templateType": "anything", "can_override": false}, "py5": {"name": "py5", "group": "Ungrouped variables", "definition": "y5/total", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["y5", "y6", "y7", "y8", "y9", "total", "PY9", "PY8", "PY7", "py6", "py5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many students are there in the school?</p>", "minValue": "total", "maxValue": "total", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A student is selected at random. What is the probability that they are in year 9? Give your answer as a fraction.</p>", "minValue": "py9", "maxValue": "py9", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Another student is selected at random from all of the students in the school. What is the probability that they are in years 5, 6 or 7? Give your answer as a fraction.</p>", "minValue": "py5+py6+py7", "maxValue": "py5+py6+py7", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Regression", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "<p>Find a regression equation.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A college compares the exam results for students in two tests. Here are the results.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Student</th>\n<th>$\\var{obj[0]}$</th>\n<th>$\\var{obj[1]}$</th>\n<th>$\\var{obj[2]}$</th>\n<th>$\\var{obj[3]}$</th>\n<th>$\\var{obj[4]}$</th>\n<th>$\\var{obj[5]}$</th>\n<th>$\\var{obj[6]}$</th>\n<th>$\\var{obj[7]}$</th>\n<th>$\\var{obj[8]}$</th>\n<th>$\\var{obj[9]}$</th>\n</tr>\n<tr>\n<th align=\"left\">First Test $(X)$</th>\n<td>$\\var{r1[0]}$</td>\n<td>$\\var{r1[1]}$</td>\n<td>$\\var{r1[2]}$</td>\n<td>$\\var{r1[3]}$</td>\n<td>$\\var{r1[4]}$</td>\n<td>$\\var{r1[5]}$</td>\n<td>$\\var{r1[6]}$</td>\n<td>$\\var{r1[7]}$</td>\n<td>$\\var{r1[8]}$</td>\n<td>$\\var{r1[9]}$</td>\n</tr>\n<tr>\n<th align=\"left\">Later Score $(Y)$</th>\n<td>$\\var{r2[0]}$</td>\n<td>$\\var{r2[1]}$</td>\n<td>$\\var{r2[2]}$</td>\n<td>$\\var{r2[3]}$</td>\n<td>$\\var{r2[4]}$</td>\n<td>$\\var{r2[5]}$</td>\n<td>$\\var{r2[6]}$</td>\n<td>$\\var{r2[7]}$</td>\n<td>$\\var{r2[8]}$</td>\n<td>$\\var{r2[9]}$</td>\n</tr>\n</tbody>\n</table>", "advice": "", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"tsqovern": {"name": "tsqovern", "group": "Ungrouped variables", "definition": "[t[0]^2/n,t[1]^2/n]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(1/n*(t[1]-spxy/ss[0]*t[0]),3)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "precround(spxy/ss[0],3)", "description": "", "templateType": "anything", "can_override": false}, "obj": {"name": "obj", "group": "Ungrouped variables", "definition": "['A','B','C','D','E','F','G','H','I','J']", "description": "", "templateType": "anything", "can_override": false}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "repeat(round(normalsample(67,8)),10)", "description": "", "templateType": "anything", "can_override": false}, "r2": {"name": "r2", "group": "Ungrouped variables", "definition": "map(round(a1+b1*x+random(-9..9)),x,r1)", "description": "", "templateType": "anything", "can_override": false}, "ss": {"name": "ss", "group": "Ungrouped variables", "definition": "[ssq[0]-t[0]^2/n,ssq[1]-t[1]^2/n]", "description": "", "templateType": "anything", "can_override": false}, "res": {"name": "res", "group": "Ungrouped variables", "definition": "map(precround(r2[x]-(a+b*r1[x]),2),x,0..n-1)", "description": "", "templateType": "anything", "can_override": false}, "ssq": {"name": "ssq", "group": "Ungrouped variables", "definition": "[sum(map(x^2,x,r1)),sum(map(x^2,x,r2))]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "10", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "templateType": "anything", "can_override": false}, "ch": {"name": "ch", "group": "Ungrouped variables", "definition": "random(0..9)", "description": "", "templateType": "anything", "can_override": false}, "spxy": {"name": "spxy", "group": "Ungrouped variables", "definition": "sxy-t[0]*t[1]/n", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "[sum(r1),sum(r2)]", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "Ungrouped variables", "definition": "r1[ch]", "description": "", "templateType": "anything", "can_override": false}, "sxy": {"name": "sxy", "group": "Ungrouped variables", "definition": "sum(map(r1[x]*r2[x],x,0..n-1))", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(0.25..0.45#0.05)", "description": "", "templateType": "anything", "can_override": false}, "ls": {"name": "ls", "group": "Ungrouped variables", "definition": "precround(a+b*sc,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["tsqovern", "a", "b", "obj", "r1", "r2", "ss", "res", "ssq", "n", "a1", "ch", "spxy", "t", "tol", "sc", "sxy", "b1", "ls"], "variable_groups": [], "functions": {"pstdev": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the equation of the regression line:</p>\n<p style=\"text-align: center;\">y = $a$ + $b$$x$</p>\n<p>Find $a$ and $b$ to 5 decimal places, then input them below to 3 decimal places.&nbsp;</p>\n<p>$b=\\;$[[0]], &nbsp; &nbsp; &nbsp;$a=\\;$[[1]] (enter both to 3 decimal places).</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b-tol", "maxValue": "b+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a-tol", "maxValue": "a+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Stratified Sampling", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>The table shows the number of students studying particular subjects in a college. (Students only study one of these courses)</p>\n<table width=\"596\" height=\"45\" border=\"1\" style=\"height: 45px;\">\n<tbody>\n<tr style=\"background-color: #8deff2;\">\n<td style=\"width: 100px; text-align: center;\">Biology</td>\n<td style=\"width: 100px; text-align: center;\">Chemistry</td>\n<td style=\"width: 100px; text-align: center;\">Physics</td>\n<td style=\"width: 100px; text-align: center;\">Biochemistry</td>\n<td style=\"width: 100px; text-align: center;\">Maths</td>\n<td style=\"width: 100px; text-align: center;\">Statistics</td>\n</tr>\n<tr style=\"background-color: #8deff2;\">\n<td style=\"width: 100px; text-align: center;\">{biol}</td>\n<td style=\"width: 100px; text-align: center;\">{chem}</td>\n<td style=\"width: 100px; text-align: center;\">{phys}</td>\n<td style=\"width: 100px; text-align: center;\">{biochem}</td>\n<td style=\"width: 100px; text-align: center;\">{maths}</td>\n<td style=\"width: 100px; text-align: center;\">{stats}</td>\n</tr>\n</tbody>\n</table>\n<p>The university wants to select a sample of {sample} students to take part in a survey.&nbsp;</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pop": {"name": "pop", "group": "Ungrouped variables", "definition": "random(2500..3000)", "description": "", "templateType": "anything", "can_override": false}, "biol": {"name": "biol", "group": "Ungrouped variables", "definition": "random(300..450)", "description": "", "templateType": "anything", "can_override": false}, "chem": {"name": "chem", "group": "Ungrouped variables", "definition": "random(300..450)", "description": "", "templateType": "anything", "can_override": false}, "phys": {"name": "phys", "group": "Ungrouped variables", "definition": "random(300..450)", "description": "", "templateType": "anything", "can_override": false}, "biochem": {"name": "biochem", "group": "Ungrouped variables", "definition": "random(300..450)\n", "description": "", "templateType": "anything", "can_override": false}, "maths": {"name": "maths", "group": "Ungrouped variables", "definition": "random(300..450)\n", "description": "", "templateType": "anything", "can_override": false}, "stats": {"name": "stats", "group": "Ungrouped variables", "definition": "pop-(biol+chem+phys+biochem+maths)\n", "description": "", "templateType": "anything", "can_override": false}, "sample": {"name": "sample", "group": "Ungrouped variables", "definition": "random(25..80)", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "(biol/pop)*100", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "(chem/pop)*100\n", "description": "", "templateType": "anything", "can_override": false}, "P3": {"name": "P3", "group": "Ungrouped variables", "definition": "(phys/pop)*100\n", "description": "", "templateType": "anything", "can_override": false}, "P4": {"name": "P4", "group": "Ungrouped variables", "definition": "(biochem/pop)*100\n", "description": "", "templateType": "anything", "can_override": false}, "P5": {"name": "P5", "group": "Ungrouped variables", "definition": "(maths/pop)*100\n", "description": "", "templateType": "anything", "can_override": false}, "P6": {"name": "P6", "group": "Ungrouped variables", "definition": "(stats/pop)*100", "description": "", "templateType": "anything", "can_override": false}, "N1": {"name": "N1", "group": "Ungrouped variables", "definition": "(P1/100)*sample", "description": "", "templateType": "anything", "can_override": false}, "N2": {"name": "N2", "group": "Ungrouped variables", "definition": "(P2/100)*sample", "description": "", "templateType": "anything", "can_override": false}, "N3": {"name": "N3", "group": "Ungrouped variables", "definition": "(P3/100)*sample", "description": "", "templateType": "anything", "can_override": false}, "N4": {"name": "N4", "group": "Ungrouped variables", "definition": "(P4/100)*sample", "description": "", "templateType": "anything", "can_override": false}, "N5": {"name": "N5", "group": "Ungrouped variables", "definition": "(P5/100)*sample", "description": "", "templateType": "anything", "can_override": false}, "N6": {"name": "N6", "group": "Ungrouped variables", "definition": "(P6/100)*sample", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pop", "biol", "chem", "phys", "biochem", "maths", "stats", "sample", "P1", "P2", "P3", "P4", "P5", "P6", "N1", "N2", "N3", "N4", "N5", "N6"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Complete the table below to show the percentage of students for each course.</p>\n<p>Give your answer to 1 decimal place.</p>\n<table width=\"505\" height=\"46\" border=\"1\" style=\"height: 46px; float: left; width: 493px;\">\n<tbody>\n<tr>\n<td style=\"width: 81px;\">Biology</td>\n<td style=\"width: 81px;\">Chemistry</td>\n<td style=\"width: 82px;\">Physics</td>\n<td style=\"width: 83px;\">Biochemistry</td>\n<td style=\"width: 83px;\">&nbsp;Maths</td>\n<td style=\"width: 83px;\">Statistics</td>\n</tr>\n<tr>\n<td style=\"width: 81px;\">[[0]]</td>\n<td style=\"width: 81px;\">[[1]]</td>\n<td style=\"width: 82px;\">[[2]]</td>\n<td style=\"width: 83px;\">[[3]]</td>\n<td style=\"width: 83px;\">[[4]]</td>\n<td style=\"width: 83px;\">[[5]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P1", "maxValue": "P2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P2", "maxValue": "P2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P3", "maxValue": "P3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P4", "maxValue": "P4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P5", "maxValue": "P5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P6", "maxValue": "P6", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Complete the table to show the number of students needed for each course in the sample. Remember to round your answers to the nearest whole number.</p>\n<table width=\"558\" height=\"32\" border=\"1\" style=\"height: 52px; width: 480px;\">\n<tbody>\n<tr>\n<td style=\"width: 51.6458px;\">Biology</td>\n<td style=\"width: 71.5729px;\">Chemistry</td>\n<td style=\"width: 51.5417px;\">Physics</td>\n<td style=\"width: 90.9688px;\">Biochemistry</td>\n<td style=\"width: 44.5104px;\">&nbsp;Maths</td>\n<td style=\"width: 75.0938px;\">Statistics</td>\n</tr>\n<tr>\n<td style=\"width: 51.6458px;\">[[0]]</td>\n<td style=\"width: 71.5729px;\">[[1]]</td>\n<td style=\"width: 51.5417px;\">[[2]]</td>\n<td style=\"width: 90.9688px;\">[[3]]</td>\n<td style=\"width: 44.5104px;\">[[4]]</td>\n<td style=\"width: 75.0938px;\">[[5]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N1-1", "maxValue": "N1+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N2-1", "maxValue": "N2+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N3-1", "maxValue": "N3+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N4-1", "maxValue": "N4+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N5-1", "maxValue": "N5+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N6-1", "maxValue": "N6+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Tree 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Marlene is learning to drive. The probability that she passes her driving test on any attempt is {pass}</p>\n<p>Answer the following questions.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pass": {"name": "pass", "group": "Ungrouped variables", "definition": "random(0.6 .. 0.9#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "pass3": {"name": "pass3", "group": "Ungrouped variables", "definition": "fail*fail*pass", "description": "", "templateType": "anything", "can_override": false}, "fail": {"name": "fail", "group": "Ungrouped variables", "definition": "1-pass", "description": "", "templateType": "anything", "can_override": false}, "pass2": {"name": "pass2", "group": "Ungrouped variables", "definition": "fail*pass", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pass", "pass3", "fail", "pass2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability that she passes at the first attemot?</p>", "minValue": "pass", "maxValue": "pass", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ol>\n<li>What is the probability that she passes at the third attempt?&nbsp;</li>\n</ol>\n<p>Hint: once she passes she won't take the test again!</p>", "minValue": "pass3", "maxValue": "pass3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "4", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability that she passes in fewer than 4 attempts?</p>", "minValue": "pass+pass2+pass3", "maxValue": "pass+pass2+pass3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "4", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "S2 EXAM Venn4", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [["question-resources/newspaper.jpg", "/srv/numbas/media/question-resources/newspaper.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": ["category: statistics", "leads to: 335, Venn Diagrams (conditional prob.)", "skill: 234, Venn Diagrams (probability)"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>This question gives some information about which newspaper is read by a group of people.&nbsp;</p>\n<p><img src=\"resources/question-resources/newspaper.jpg\" width=\"494\" height=\"247\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"diagram": {"name": "diagram", "group": "Ungrouped variables", "definition": "eukleides(\"A Venn diagram with {justA} in just The Times, {justB} in just The Guardian, {both} in both, and {neither} in neither\",\n[\ncircle(point(0,0),2) color1 filled opacity(0.5),\npoint(-1,2) label(\"The Guardian\",deg(180)),\ncircle(point(3,0),2) color2 filled opacity(0.5),\npoint(4,2) label(\"The Independent\",deg(0)),\npoint(0,0) label(justA,deg(180)),\npoint(3,0) label(justB,deg(0)),\npoint(1.5,0) label(both,0),\npoint(6,0) 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