// Numbas version: exam_results_page_options {"name": "S2 EXAM Binomial Distribution 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "S2 EXAM Binomial Distribution 1", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Please give your answer to at least 3 decimal places.

\n

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.

\n

Hint: for this question use the binomial distribution.

\n

", "advice": "", "rulesets": {}, "extensions": [], "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": "

probability that r = 3

", "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": "

the probability that an individual student cycles to college

", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "3", "description": "

more than r of the students cycle to college

", "templateType": "anything", "can_override": false}, "pr1": {"name": "pr1", "group": "Ungrouped variables", "definition": "n*p*q^(n-1)", "description": "

probability that r = 1

", "templateType": "anything", "can_override": false}, "pr2": {"name": "pr2", "group": "Ungrouped variables", "definition": "((n*(n-1))/2)*(p^2)*q^(n-2)", "description": "

probability that r = 2

", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(6..12)", "description": "

sample size

", "templateType": "anything", "can_override": false}, "pr0": {"name": "pr0", "group": "Ungrouped variables", "definition": "q^n", "description": "

probability that r = 0

", "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": "

percentage of students that cycle to college

", "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": "

probability tha an individual does not cycle to college

", "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": "

Calculate the probability that none of the Oldcastle $\\var{n}$ students read the student newspaper.

", "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": "

Calculate the probability that at least $\\var{r}$ of the $\\var{n}$ students read the student newspaper.

", "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", "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/"}]}]}], "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/"}]}