// Numbas version: exam_results_page_options
{"name": "Poisson_1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Poisson_1", "extensions": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["m", "n", "p", "o"], "variables": {"o": {"name": "o", "description": "", "group": "Ungrouped variables", "definition": "fact({n})", "templateType": "anything"}, "p": {"name": "p", "description": "", "group": "Ungrouped variables", "definition": "e^(-{m})*({m}^{n})/fact({n})", "templateType": "anything"}, "n": {"name": "n", "description": "", "group": "Ungrouped variables", "definition": "random(1..8#1)", "templateType": "randrange"}, "m": {"name": "m", "description": "", "group": "Ungrouped variables", "definition": "random(5..15#1)", "templateType": "randrange"}}, "preamble": {"css": "", "js": ""}, "statement": "<p>Let X be the number of cars per minute passing a certain point on the road.</p>\n<p>Assume X has a Poisson distribution with mean \\(\\var{m}\\).</p>", "advice": "<p>The Poisson distribution \\(P(X=k)=\\frac{e^{-\\lambda}\\lambda^k}{k!}\\)</p>\n<p>In this problem \\(\\lambda=\\var{m}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=\\var{n})=\\frac{e^{-\\var{m}}*\\var{m}^{\\var{n}}}{\\var{n}!}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=\\var{n})=\\frac{\\simplify{e^{-{m}}*{m}^{n}}}{\\var{o}}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=\\var{n})=\\var{p}\\)</p>", "variable_groups": [], "functions": {}, "parts": [{"gaps": [{"precisionType": "dp", "allowFractions": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "strictPrecision": false, "showPrecisionHint": false, "correctAnswerStyle": "plain", "scripts": {}, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{p}", "variableReplacements": [], "minValue": "{p}", "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "precisionPartialCredit": 0}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "prompt": "<p>Calculate, correct to three decimal places, the probability that exactly \\(\\var{n}\\) cars pass in a particular minute. &nbsp; &nbsp;[[0]]</p>", "type": "gapfill"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}