// Numbas version: exam_results_page_options
{"name": "Poisson_2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Poisson_2", "extensions": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["m", "n", "p", "p_0", "p_1", "p_2", "p_3", "p_4", "p_5"], "variables": {"n": {"name": "n", "description": "", "group": "Ungrouped variables", "definition": "random(4..5#1)", "templateType": "randrange"}, "p_4": {"name": "p_4", "description": "", "group": "Ungrouped variables", "definition": "(e^(-{m})*{m}^4)/24", "templateType": "anything"}, "p_2": {"name": "p_2", "description": "", "group": "Ungrouped variables", "definition": "(e^(-{m})*{m}^2)/2\n", "templateType": "anything"}, "p_0": {"name": "p_0", "description": "", "group": "Ungrouped variables", "definition": "e^(-{m})", "templateType": "anything"}, "p": {"name": "p", "description": "", "group": "Ungrouped variables", "definition": "if(n<5,{p_0}+{p_1}+{p_2}+{p_3}+{p_4},{p_0}+{p_1}+{p_2}+{p_3}+{p_4}+{p_5})", "templateType": "anything"}, "p_1": {"name": "p_1", "description": "", "group": "Ungrouped variables", "definition": "e^(-{m})*({m})", "templateType": "anything"}, "m": {"name": "m", "description": "", "group": "Ungrouped variables", "definition": "random(3..12#1)", "templateType": "randrange"}, "p_3": {"name": "p_3", "description": "", "group": "Ungrouped variables", "definition": "(e^(-{m})*{m}^3)/6", "templateType": "anything"}, "p_5": {"name": "p_5", "description": "", "group": "Ungrouped variables", "definition": "(e^(-{m})*{m}^5)/120", "templateType": "anything"}}, "preamble": {"css": "", "js": ""}, "statement": "<p>A&nbsp;telephone switchboard can make&nbsp;\\(\\var{m}\\) connections&nbsp;per second&nbsp;on average.&nbsp;</p>\n<p></p>\n<p></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>P(at most \\(\\var{n}\\) connections) = \\(P(X\\le\\var{n})\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X\\le\\var{n})=P(X=0)+P(X=1)+...P(X=\\var{n})\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=0)=\\var{p_0}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=1)=\\var{p_1}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=2)=\\var{p_2}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=3)=\\var{p_3}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=4)=\\var{p_4}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X=5)=\\var{p_5}\\)</p>\n<p style=\"padding-left: 90px;\">\\(P(X\\le\\var{n})=\\var{p}\\)</p>", "functions": {}, "variable_groups": [], "parts": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"precisionType": "dp", "allowFractions": false, "maxValue": "{p}", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "strictPrecision": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "minValue": "{p}", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precision": "3", "mustBeReduced": false, "marks": 1, "precisionPartialCredit": 0}], "marks": 0, "prompt": "<p>Calculate, correct to three decimal places, the probability that the switchboard will make at most&nbsp;\\(\\var{n}\\) connections&nbsp;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/"}]}