// Numbas version: finer_feedback_settings
{"name": "MA0371 Resit Exam", "metadata": {"description": "", "licence": "None specified"}, "duration": 7200, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "variable_overrides": [[], [], [], [], []], "questions": [{"name": "PMCC and Regression Line", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Knapp", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14987/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The following table shows $8$ pairs of data values for the variables $x$ and $y$:</p>\n<p></p>\n<table width=\"684\" height=\"90\" style=\"height: 105px; width: 684px; border-style: solid; border-color: #000000; background-color: #f0f0f0; margin-left: auto; margin-right: auto;\" border=\"2cm\" cellspacing=\"5cm\" cellpadding=\"2cm\"><caption>Data Values</caption>\n<tbody>\n<tr style=\"height: 34px;\">\n<td style=\"width: 60.65px; height: 34px; text-align: center;\">$x$</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x1}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x2}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x3}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x4}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x5}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x6}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{x7}</td>\n<td style=\"width: 59.675px; height: 34px; text-align: center;\">{x8}</td>\n</tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 60.65px; height: 34px; text-align: center;\">$y$</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y1}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y2}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y3}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y4}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y5}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y6}</td>\n<td style=\"width: 59.525px; height: 34px; text-align: center;\">{y7}</td>\n<td style=\"width: 59.675px; height: 34px; text-align: center;\">{y8}</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "<p><strong>(a)</strong></p>\n<p>$r = \\var{rround}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>$a = \\var{around}$</p>\n<p>$b = \\var{bround}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(x1..5)", "description": "", "templateType": "anything", "can_override": false}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(x2..7)", "description": "", "templateType": "anything", "can_override": false}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(x3..10)", "description": "", "templateType": "anything", "can_override": false}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(x4..13)", "description": "", "templateType": "anything", "can_override": false}, "x6": {"name": "x6", "group": "Ungrouped variables", "definition": "random(x5..15)", "description": "", "templateType": "anything", "can_override": false}, "x7": {"name": "x7", "group": "Ungrouped variables", "definition": "random(x6..18)", "description": "", "templateType": "anything", "can_override": false}, "x8": {"name": "x8", "group": "Ungrouped variables", "definition": "random(x7..20)", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(40..50)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(40..50)", "description": "", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(35..40)", "description": "", "templateType": "anything", "can_override": false}, "y4": {"name": "y4", "group": "Ungrouped variables", "definition": "random(35..40)", "description": "", "templateType": "anything", "can_override": false}, "y5": {"name": "y5", "group": "Ungrouped variables", "definition": "random(30..35)", "description": "", "templateType": "anything", "can_override": false}, "y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(30..35)", "description": "", "templateType": "anything", "can_override": false}, "y8": {"name": "y8", "group": "Ungrouped variables", "definition": "random(20..30)", "description": "", "templateType": "anything", "can_override": false}, "y7": {"name": "y7", "group": "Ungrouped variables", "definition": "random(20..30)", "description": "", "templateType": "anything", "can_override": false}, "sumx": {"name": "sumx", "group": "Ungrouped variables", "definition": "x1+x2+x3+x4+x5+x6+x7+x8", "description": "", "templateType": "anything", "can_override": false}, "sumy": {"name": "sumy", "group": "Ungrouped variables", "definition": "y1+y2+y3+y4+y5+y6+y7+y8", "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", "description": "", "templateType": "anything", "can_override": false}, "sumx2": {"name": "sumx2", "group": "Ungrouped variables", "definition": "x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2", "description": "", "templateType": "anything", "can_override": false}, "sumy2": {"name": "sumy2", "group": "Ungrouped variables", "definition": "y1^2+y2^2+y3^2+y4^2+y5^2+y6^2+y7^2+y8^2", "description": "", "templateType": "anything", "can_override": false}, "sxx": {"name": "sxx", "group": "Ungrouped variables", "definition": "sumx2-(sumx)^2/8", "description": "", "templateType": "anything", "can_override": false}, "syy": {"name": "syy", "group": "Ungrouped variables", "definition": "sumy2-(sumy)^2/8", "description": "", "templateType": "anything", "can_override": false}, "sxy": {"name": "sxy", "group": "Ungrouped variables", "definition": "sumxy-(sumx)*(sumy)/8", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "sxy/(sqrt(sxx*syy))", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "(sumy)/8-b*(sumx)/8", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "sxy/sxx", "description": "", "templateType": "anything", "can_override": false}, "rround": {"name": "rround", "group": "Ungrouped variables", "definition": "precround(r,4)", "description": "", "templateType": "anything", "can_override": false}, "around": {"name": "around", "group": "Ungrouped variables", "definition": "precround(a,2)", "description": "", "templateType": "anything", "can_override": false}, "bround": {"name": "bround", "group": "Ungrouped variables", "definition": "precround(b,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "y1", "y2", "y3", "y4", "y5", "y6", "y7", "y8", "sumx", "sumy", "sumxy", "sumx2", "sumy2", "sxx", "syy", "sxy", "r", "a", "b", "rround", "around", "bround"], "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>Find the product moment correlation coefficient $r$.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "r", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{r}", "maxValue": "{r}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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>Find the values of $a$ and $b$ such that the least squares regression line of $y$ on $x$ is given by $y=a+bx$.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "a", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a}", "maxValue": "{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "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": true, "customName": "b", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Averages and Spread", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Knapp", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14987/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The table below shows the ages in years, of a random sample of $10$ people in a shop:</p>\n<p></p>\n<table width=\"590\" height=\"76\" style=\"height: 76px; width: 590px; border-style: solid; border-color: #000000; background-color: #f0f0f0; margin-left: auto; margin-right: auto;\" border=\"2cm\" cellpadding=\"2cm\" cellspacing=\"5cm\"><caption>Ages</caption>\n<tbody>\n<tr>\n<td style=\"width: 59.8875px; text-align: center;\">{list[0]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[1]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[2]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[3]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[4]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[5]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[6]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[7]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[8]}</td>\n<td style=\"width: 59.8875px; text-align: center;\">{list[9]}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>(a)</strong></p>\n<p>The mean age is $\\var{meanround}$</p>\n<p>The median age is $\\var{medianround}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>The standard deviation of ages is $\\var{stdround}$</p>\n<p>The inter-quartile range of ages is $\\var{iqr}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"list": {"name": "list", "group": "Ungrouped variables", "definition": "repeat(random(5..u),10)", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(50..75)", "description": "", "templateType": "anything", "can_override": false}, "median": {"name": "median", "group": "Ungrouped variables", "definition": "median(list)", "description": "", "templateType": "anything", "can_override": false}, "mean": {"name": "mean", "group": "Ungrouped variables", "definition": "mean(list)", "description": "", "templateType": "anything", "can_override": false}, "stddev": {"name": "stddev", "group": "Ungrouped variables", "definition": "stdev(list)", "description": "", "templateType": "anything", "can_override": false}, "quartiles": {"name": "quartiles", "group": "Ungrouped variables", "definition": "quartiles(list)", "description": "", "templateType": "anything", "can_override": false}, "iqr": {"name": "iqr", "group": "Ungrouped variables", "definition": "quartiles[2]-quartiles[0]", "description": "", "templateType": "anything", "can_override": false}, "meanround": {"name": "meanround", "group": "Ungrouped variables", "definition": "precround(mean,1)", "description": "", "templateType": "anything", "can_override": false}, "medianround": {"name": "medianround", "group": "Ungrouped variables", "definition": "precround(median,1)", "description": "", "templateType": "anything", "can_override": false}, "stdround": {"name": "stdround", "group": "Ungrouped variables", "definition": "precround(stddev,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["list", "u", "median", "mean", "stddev", "quartiles", "iqr", "meanround", "medianround", "stdround"], "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>Calculate the mean&nbsp;<span style=\"text-decoration: underline;\">and</span> median of the data.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "mean", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{mean}", "maxValue": "{mean}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "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": true, "customName": "median", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{median}", "maxValue": "{median}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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>Calculate the standard deviation&nbsp;<span style=\"text-decoration: underline;\">and</span> inter-quartile range of the data.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "stddev", "marks": "7.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{stddev}", "maxValue": "{stddev}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "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": true, "customName": "iqr", "marks": "7.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{iqr}", "maxValue": "{iqr}", "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": "Probability Venn Diagram", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "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/"}, {"name": "Chris Knapp", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14987/"}], "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>$100$ students were asked whether they have a dog or a cat at home. The results are presented in the Venn diagram below:</p>\n<p style=\"text-align: center;\">{max_width(30,diagram)}</p>\n<p>Find the following probabilities, giving your answers as fractions in their simplest forms.</p>", "advice": "<p><strong>(a)</strong></p>\n<p>$P(C \\cap D) = \\var[fractionnumbers]{prob1}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>$P(C^c \\cup D^c) = \\var[fractionnumbers]{prob2}$</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>$P((C \\cup D)^c\\cap D) = \\var[fractionnumbs]{prob3}$</p>", "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 Mathematics, {justB} in just Physics, {both} in both, and {neither} in neither\",\n[\ncircle(point(0,0),2) color5 filled opacity(0.5),\npoint(-1,2) label(\"Cat (C)\",deg(180)),\ncircle(point(3,0),2) color2 filled opacity(0.5),\npoint(4,2) label(\"Dog (D)\",deg(0)),\npoint(0,0) label(justA,deg(180)),\npoint(3,0) label(justB,deg(0)),\npoint(1.5,0) label(both,0),\npoint(5.5,0) label(neither)\n],\n[\"justA\":justA,\"justB\":justB,\"both\":both,\"neither\":neither]\n)", "description": "", "templateType": "anything", "can_override": false}, "justA": {"name": "justA", "group": "Ungrouped variables", "definition": "group1[0]", "description": "", "templateType": "anything", "can_override": false}, "justB": {"name": "justB", "group": "Ungrouped variables", "definition": "group1[1]", "description": "", "templateType": "anything", "can_override": false}, "both": {"name": "both", "group": "Ungrouped variables", "definition": "group1[2]", "description": "", "templateType": "anything", "can_override": false}, "neither": {"name": "neither", "group": "Ungrouped variables", "definition": "group1[3]", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "(justA+justB)/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "pb": {"name": "pb", "group": "Ungrouped variables", "definition": "both/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "pfrench": {"name": "pfrench", "group": "Ungrouped variables", "definition": "justB/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "pneither": {"name": "pneither", "group": "Ungrouped variables", "definition": "neither/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "penglish": {"name": "penglish", "group": "Ungrouped variables", "definition": "justA/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "group1": {"name": "group1", "group": "Ungrouped variables", "definition": "[a,b,c,d]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5..30)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "100-(a+b+c)", "description": "", "templateType": "anything", "can_override": false}, "prob1": {"name": "prob1", "group": "Ungrouped variables", "definition": "both/100", "description": "", "templateType": "anything", "can_override": false}, "prob2": {"name": "prob2", "group": "Ungrouped variables", "definition": "(100-both)/100", "description": "", "templateType": "anything", "can_override": false}, "prob3": {"name": "prob3", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "d>0", "maxRuns": 100}, "ungrouped_variables": ["justA", "justB", "both", "neither", "diagram", "p", "pb", "pfrench", "pneither", "penglish", "group1", "a", "b", "c", "d", "prob1", "prob2", "prob3"], "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>$P(C \\cap D)$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "prob1", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{prob1}", "maxValue": "{prob1}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": 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>$P(C^c \\cup D^c)$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "prob2", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{prob2}", "maxValue": "{prob2}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": 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>$P((C \\cup D)^c\\cap D)$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "prob3", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{prob3}", "maxValue": "{prob3}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Probability -Tree Diagram", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Cards.jpg", "/srv/numbas/media/question-resources/Cards.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Knapp", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14987/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A student picks two cards without replacement from a standard pack of $52$ playing cards.&nbsp;</p>\n<p><em>Note: a pack of playing cards comprises 52 cards, split equally into four suits (Hearts, Diamonds, Spades, Clubs). Each suit has 13 cards (Ace, 2, 3, $\\ldots$, 9, 10, Jack, Queen, King).</em><img src=\"resources/question-resources/Cards.jpg\" width=\"395\" height=\"263\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Calculate the following probabilities, giving your answers as fractions in their simplest forms.</p>", "advice": "<p><strong>(a)</strong></p>\n<p>The probability that the student picks two $\\var{numbers}$s is $\\var[fractionnumbers]{samenumbers}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>The probability that the student picks two $\\var{suits}$ is $\\var[fractionnumbers]{samesuit}$</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>The probability that the student picks two cards which add up to $25$ is $\\var[fractionnumbers]{sumto25}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "random(2,3,4,5,6,7,8,9,10,\"Jack\",\"Queen\",\"King\",\"Ace\")", "description": "", "templateType": "anything", "can_override": false}, "suits": {"name": "suits", "group": "Ungrouped variables", "definition": "random(\"Hearts\", \"Clubs\", \"Diamonds\", \"Spades\")", "description": "", "templateType": "anything", "can_override": false}, "samenumbers": {"name": "samenumbers", "group": "Ungrouped variables", "definition": "1/221", "description": "", "templateType": "anything", "can_override": false}, "samesuit": {"name": "samesuit", "group": "Ungrouped variables", "definition": "1/17", "description": "", "templateType": "anything", "can_override": false}, "sumto25": {"name": "sumto25", "group": "Ungrouped variables", "definition": "8/663", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbers", "suits", "samenumbers", "samesuit", "sumto25"], "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>Find the probability that the student picks two $\\var{numbers}$s.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "samenumbers", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1/221", "maxValue": "1/221", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": 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>Find the probability that the student picks two $\\var{suits}$.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "same suit", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1/17", "maxValue": "1/17", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": 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>Let an Ace, Jack, Queen and King have numerical values of $1, 11, 12$ and $13$ respectively.</p>\n<p>Find the probability that the student picks two cards which add up to $25$.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "sumto25", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "8/663", "maxValue": "8/663", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Chris's copy of Binomial Hypothesis Test", "extensions": ["stats"], "custom_part_types": [], "resources": [["question-resources/charlescoin.jpg", "/srv/numbas/media/question-resources/charlescoin.jpg"], ["question-resources/charlescoin_4JVgsBb.jpg", "/srv/numbas/media/question-resources/charlescoin_4JVgsBb.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Knapp", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14987/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A coin is tossed $\\var{flips}$ times, and lands on heads $\\var{heads}$ times.&nbsp;</p>\n<p><img src=\"resources/question-resources/charlescoin_4JVgsBb.jpg\" width=\"232\" height=\"232\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Use a hypothesis test with a $\\var{siglev}$% significance level to determine whether there is sufficient evidence to suggest the coin is biased in favour of heads. Let $X=$ the number of heads the coin lands on.</p>\n<p></p>", "advice": "<p>Let $X=$ the number of heads the coin lands on.</p>\n<p>Let $p=$ the probability of landing on a heads.</p>\n<p></p>\n<p>$H_0: p = \\frac{1}{2}$</p>\n<p>$H_1: p &gt; \\frac{1}{2}$</p>\n<p></p>\n<p>Assume $H_0$ is true, then $X \\sim B( \\var{flips}, \\frac{1}{2})$.</p>\n<p></p>\n<p>Now, $P(X &ge; \\var{heads}) = \\var{roundteststat}$.</p>\n<p>This is $\\var{correctmoreless}$ than the significance level of $\\var{siglev}$%, therefore there is $\\var{suffcorrect}$ evidence to reject $H_0$.</p>\n<p></p>\n<p>This means there $\\var{reasoncorrect}$ reason to suggest the coin is biased in favour of heads.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"flips": {"name": "flips", "group": "Ungrouped variables", "definition": "random(20..40)", "description": "", "templateType": "anything", "can_override": false}, "heads": {"name": "heads", "group": "Ungrouped variables", "definition": "random(precround(flips/2+5,0)..flips-3)", "description": "", "templateType": "anything", "can_override": false}, "siglev": {"name": "siglev", "group": "Ungrouped variables", "definition": "random(1,2,5,10)", "description": "", "templateType": "anything", "can_override": false}, "teststat": {"name": "teststat", "group": "Ungrouped variables", "definition": "1-binomialcdf(heads-1,flips,1/2)", "description": "", "templateType": "anything", "can_override": false}, "correctmoreless": {"name": "correctmoreless", "group": "Ungrouped variables", "definition": "if(teststat<siglevpercent, \"less than\", \"more than\")", "description": "", "templateType": "anything", "can_override": false}, "wrongmoreless": {"name": "wrongmoreless", "group": "Ungrouped variables", "definition": "if(correctmoreless=\"less than\", \"more than\", \"less than\")", "description": "", "templateType": "anything", "can_override": false}, "suffcorrect": {"name": "suffcorrect", "group": "Ungrouped variables", "definition": "if(correctmoreless=\"less than\", \"sufficient\", \"insufficient\")", "description": "", "templateType": "anything", "can_override": false}, "suffwrong": {"name": "suffwrong", "group": "Ungrouped variables", "definition": "if(suffcorrect=\"sufficient\", \"insufficient\", \"sufficient\")", "description": "", "templateType": "anything", "can_override": false}, "siglevpercent": {"name": "siglevpercent", "group": "Ungrouped variables", "definition": "siglev/100", "description": "", "templateType": "anything", "can_override": false}, "reasoncorrect": {"name": "reasoncorrect", "group": "Ungrouped variables", "definition": "if(suffcorrect=\"sufficient\", \"is\", \"is no\")", "description": "", "templateType": "anything", "can_override": false}, "reasonwrong": {"name": "reasonwrong", "group": "Ungrouped variables", "definition": "if(reasoncorrect=\"is\", \"is not\", \"is\")", "description": "", "templateType": "anything", "can_override": false}, "roundteststat": {"name": "roundteststat", "group": "Ungrouped variables", "definition": "precround(teststat,7)", "description": "", "templateType": "anything", "can_override": false}, "space": {"name": "space", "group": "Ungrouped variables", "definition": "\"space for comment\"", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["flips", "heads", "siglev", "teststat", "correctmoreless", "wrongmoreless", "suffcorrect", "suffwrong", "siglevpercent", "reasoncorrect", "reasonwrong", "roundteststat", "space"], "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, "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "null hypothesis sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["=", "&ne;", "&gt;", "&lt;"], "matrix": ["2", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "alt hypothesis sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["=", "&ne;", "&lt;", "&gt;"], "matrix": [0, 0, 0, "2"], "distractors": ["", "", "", ""]}, {"type": "numberentry", "useCustomName": true, "customName": "n", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{flips}", "maxValue": "{flips}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "p", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1/2", "maxValue": "1/2", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "prob", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["&ge;", "&le;", "&lt;", "&gt;"], "matrix": ["2", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "numberentry", "useCustomName": true, "customName": "heads", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{heads}", "maxValue": "{heads}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "teststat", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{teststat}", "maxValue": "{teststat}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "7", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "moreless", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{correctmoreless}", "{wrongmoreless}"], "matrix": ["2", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "sufficient", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 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