// Numbas version: exam_results_page_options
{"name": "Poisson Distribution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Poisson Distribution", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p></p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p>\n<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n</p>\n<p></p>", "advice": "<script id=\"th-iframe-script\" src=\"chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js\"></script>\n<p>Here are some tips on how to set out your work, as well as how to complete the questions. None of the answers given below have been rounded to what the question states.&nbsp;</p>\n<p><strong>Question 1</strong></p>\n<p>1a: $X\\sim Po(\\var{Lambda3})$</p>\n<p>(i) $P(X=x)=P(X=\\var{x5})=\\frac{e^{-\\var{Lambda3}}\\times\\var{Lambda3}^{\\var{x5}}}{\\var{x5}!}=\\var{Ans5}$</p>\n<p>(ii) $P(X=x)=P(X=\\var{x6})=\\frac{e^{-\\var{Lambda3}}\\times\\var{Lambda3}^{\\var{x6}}}{\\var{x6}!}=\\var{Ans6}$</p>\n<p>(iii) $P(X=x)=P(X=\\var{x7})=\\frac{e^{-\\var{Lambda3}}\\times\\var{Lambda3}^{\\var{x7}}}{\\var{x7}!}=\\var{Ans7}$</p>\n<p></p>\n<p>1b:&nbsp;$X\\sim Po(\\var{Lambda4})$</p>\n<p>(i) $P(X=x)=P(X&lt;\\var{x8})=P(X=0)+P(X=1)+P(X=2)=\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^0} {0!}+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^1} {1!}+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^2} {2!}=\\var{Ans8}$</p>\n<p>(ii)&nbsp;$P(X=x)=P(X\\leq\\var{x9})=P(X=0)+P(X=1)+...+P(X={\\var{x9}})=\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^0} {0!}+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^1} {1!}+...+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^{\\var{x9}}} {\\var{x9}!}=\\var{Ans9}$</p>\n<p>(iii)&nbsp;$P(X=x)=P(X&gt;\\var{x10})=1-P(X\\leq\\var{x10})=1-(P(X=0)+P(X=1)+...+P(X={\\var{x10}}))=1-(\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^0} {0!}+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^1} {1!}+...+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^{\\var{x10}}} {\\var{x10}!})=\\var{Ans10}$</p>\n<p>(iv)$P(X=x)=P(X\\geq\\var{x11})=1-P(X&lt;\\var{x11})=1-(P(X=0)+P(X=1)+...+P(X={5}))=1-(\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^0} {0!}+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^1} {1!}+...+\\frac{e^{-\\var{Lambda4}}\\times\\var{Lambda4}^{5}} {5!})=\\var{Ans11}$</p>\n<p><strong>Question 2</strong></p>\n<p>2a:&nbsp;$\\lambda=rate&nbsp; \\times hours = \\var{rate2} \\times 1 = \\var{rate2} \\therefore X\\sim Po(\\var{rate2})$</p>\n<p>(i) $P(X=x) = P(X=\\var{xx1})=\\frac{e^{-\\var{rate2}}\\times\\var{rate2}^\\var{xx1}}{\\var{xx1}!}=\\var{Ansxx}$</p>\n<p></p>\n<p>2b:&nbsp;$\\lambda=rate&nbsp; \\times hours =rate&nbsp; \\times \\frac{mins}{60} = \\var{rate}\\times\\frac{\\var{mins}}{60}=\\var{Lambda1}&nbsp; \\therefore X\\sim Po(\\var{Lambda1})$</p>\n<p>(i)&nbsp;$P(X=x) = P(X=\\var{x1})=\\frac{e^{-\\var{Lambda1}}\\times\\var{Lambda1}^\\var{x1}}{\\var{x1}!}=\\var{Ans1}$</p>\n<p>(ii)&nbsp;$P(X=x) = P(X\\geq\\var{x2})=1-P(X&lt;\\var{x2})=1-(P(X=0)+P(X=1)+...+P(X={3}))=1-(\\frac{e^{-\\var{Lambda1}}\\times\\var{Lambda1}^0} {0!}+\\frac{e^{-\\var{Lambda1}}\\times\\var{Lambda1}^1} {1!}+...+\\frac{e^{-\\var{Lambda1}}\\times\\var{Lambda1}^{3}} {3!})=\\var{Ans2}$</p>\n<p></p>\n<p>2c:&nbsp;$\\lambda=rate&nbsp; \\times hours=rate&nbsp; \\times \\frac{mins}{60} = \\var{rate}\\times\\frac{\\var{Totalmins}}{60}=\\var{Lambda1}&nbsp; \\therefore X\\sim Po(\\var{Lambda1})$</p>\n<p>(i) This is the time difference in minutes, that the rate of patients arrives within.&nbsp;</p>\n<p>(ii) $P(X=x) = P(X\\geq1)=1-P(X&lt;1)=1-P(X=0)=1-\\frac{e^{-\\var{Lambda1}}\\times\\var{Lambda1}^0} {0!}=\\var{Ans4}$</p>", "rulesets": {}, "extensions": [], "variables": {"rate": {"name": "rate", "group": "Question 2a(i)", "definition": "random(2 .. 5#1)", "description": "", "templateType": "randrange"}, "Timehrs": {"name": "Timehrs", "group": "Question 2b", "definition": "random(11 .. 13#1)", "description": "", "templateType": "randrange"}, "Daypart": {"name": "Daypart", "group": "Question 2b", "definition": "if(Timehrs>11,\"pm\",\"am\")", "description": "", "templateType": "anything"}, "Ans10": {"name": "Ans10", "group": "Question 1b", "definition": "1-(if(x10=2,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!), if(x10=3,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!),if(x10=4,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)++((e^(-Lambda4) * Lambda4^4)/4!),if(x10=5,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!)+((e^(-Lambda4) * Lambda4^5)/5!),0)))))", "description": "", "templateType": "anything"}, "Ans5": {"name": "Ans5", "group": "Question 1a", "definition": "(e^(-Lambda3) *Lambda3^x5)/x5!", "description": "", "templateType": "anything"}, "Totalmins": {"name": "Totalmins", "group": "Question 2b", "definition": "Hours*60", "description": "", "templateType": "anything"}, "x11": {"name": "x11", "group": "Question 1b", "definition": "6", "description": "", "templateType": "number"}, "Lambda3": {"name": "Lambda3", "group": "Question 1a", "definition": "random(1 .. 5#0.1)", "description": "", "templateType": "randrange"}, "xx1": {"name": "xx1", "group": "Question 2a(i)", "definition": "random(1 .. 5#1)", "description": "", "templateType": "randrange"}, "rate2": {"name": "rate2", "group": "Question 2a(i)", "definition": "random(2 .. 7#1)", "description": "", "templateType": "randrange"}, "Ans8": {"name": "Ans8", "group": "Question 1b", "definition": "if(x8=2,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!), if(x8=3,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!),if(x8=4,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!),if(x8=5,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!),0))))", "description": "", "templateType": "anything"}, "Ansxx": {"name": "Ansxx", "group": "Question 2a(i)", "definition": "(e^(-rate2) * rate2^ xx1)/xx1!", "description": "", "templateType": "anything"}, "Totaltime": {"name": "Totaltime", "group": "Question 2b", "definition": "Timehrs+(Timeminsno/100)", "description": "", "templateType": "anything"}, "Timemins": {"name": "Timemins", "group": "Question 2b", "definition": "random(15 .. 45#15)", "description": "", "templateType": "randrange"}, "Ans9": {"name": "Ans9", "group": "Question 1b", "definition": "if(x9=2,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!), if(x9=3,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!),if(x9=4,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!),if(x9=5,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!)+((e^(-Lambda4) * Lambda4^5)/5!),0))))", "description": "", "templateType": "anything"}, "mins": {"name": "mins", "group": "Question 2a(i)", "definition": "random(30 .. 120#30)", "description": "", "templateType": "randrange"}, "Hours": {"name": "Hours", "group": "Question 2b", "definition": "Totaltime-11", "description": "", "templateType": "anything"}, "x7": {"name": "x7", "group": "Question 1a", "definition": "random(5 .. 5#1)", "description": "", "templateType": "randrange"}, "Lambda1": {"name": "Lambda1", "group": "Question 2a(i)", "definition": "hrs*rate", "description": "", "templateType": "anything"}, "x3": {"name": "x3", "group": "Question 2b", "definition": "0", "description": "", "templateType": "anything"}, "x8": {"name": "x8", "group": "Question 1b", "definition": "3", "description": "", "templateType": "number"}, "Ans2": {"name": "Ans2", "group": "Question 2a(ii)", "definition": "1-(if(x2=2,((e^(-Lambda1) * Lambda1^0)/0!)+((e^(-Lambda1) * Lambda1^1)/1!), if(x2=3,((e^(-Lambda1) * Lambda1^0)/0!)+((e^(-Lambda1) * Lambda1^1)/1!)+((e^(-Lambda1) * Lambda1^2)/2!),if(x2=4,((e^(-Lambda1) * Lambda1^0)/0!)+((e^(-Lambda1) * Lambda1^1)/1!)+((e^(-Lambda1) * Lambda1^2)/2!)+((e^(-Lambda1) * Lambda1^3)/3!),if(x2=5,((e^(-Lambda1) * Lambda1^0)/0!)+((e^(-Lambda1) * Lambda1^1)/1!)+((e^(-Lambda1) * Lambda1^2)/2!)+((e^(-Lambda1) * Lambda1^3)/3!)+((e^(-Lambda1) * Lambda1^4)/4!), if(x2=6,(e^(-Lambda1) * Lambda1^0)/0!)+((e^(-Lambda1) * Lambda1^1)/1!)+((e^(-Lambda1) * Lambda1^2)/2!)+((e^(-Lambda1) * Lambda1^3)/3!)+((e^(-Lambda1) * Lambda1^4)/4!)+((e^(-Lambda1) * Lambda1^5)/5!),0)))))", "description": "", "templateType": "anything"}, "x5": {"name": "x5", "group": "Question 1a", "definition": "random(1 .. 2#1)", "description": "", "templateType": "randrange"}, "Lambda2": {"name": "Lambda2", "group": "Question 2b", "definition": "Hours*rate", "description": "", "templateType": "anything"}, "x10": {"name": "x10", "group": "Question 1b", "definition": "5", "description": "", "templateType": "number"}, "x4": {"name": "x4", "group": "Question 1a", "definition": "random(1 .. 6#1)", "description": "", "templateType": "randrange"}, "Ans11": {"name": "Ans11", "group": "Question 1b", "definition": "1-(if(x11=2,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!), if(x11=3,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!), if(x11=4,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!), if(x11=5,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!),if(x11=6,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!)+((e^(-Lambda4) *Lambda4^5)/5!),0))))))", "description": "<p>(if(x11=2,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!), if(x11=3,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!), if(x11=4,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!), if(x11=5,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!),if(x11=6,((e^(-Lambda4) * Lambda4^0)/0!)+((e^(-Lambda4) * Lambda4^1)/1!)+((e^(-Lambda4) * Lambda4^2)/2!)+((e^(-Lambda4) * Lambda4^3)/3!)+((e^(-Lambda4) * Lambda4^4)/4!)+((e^(-Lambda4) *Lambda4^5)/5!),0))))))</p>", "templateType": "anything"}, "x2": {"name": "x2", "group": "Question 2a(ii)", "definition": "random(3 .. 6#1)", "description": "", "templateType": "randrange"}, "Ans3": {"name": "Ans3", "group": "Question 2b", "definition": "Totalmins", "description": "", "templateType": "anything"}, "Ans1": {"name": "Ans1", "group": "Question 2a(i)", "definition": "(e^(-Lambda1) * Lambda1^ x1)/x1!", "description": "", "templateType": "anything"}, "Lambda4": {"name": "Lambda4", "group": "Question 1b", "definition": "random(1 .. 5#0.1)", "description": "", "templateType": "randrange"}, "Ans4": {"name": "Ans4", "group": "Question 2b", "definition": "1-((e^(-Lambda2) * Lambda2^x3)/x3!)", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "Question 2a(i)", "definition": "random(2 .. 3#1)", "description": "", "templateType": "randrange"}, "Timeminsno": {"name": "Timeminsno", "group": "Question 2b", "definition": "(Timemins * 100)/60", "description": "", "templateType": "anything"}, "Ans7": {"name": "Ans7", "group": "Question 1a", "definition": "(e^(-Lambda3) *Lambda3^x7)/x7!", "description": "", "templateType": "anything"}, "Ans6": {"name": "Ans6", "group": "Question 1a", "definition": "(e^(-Lambda3) *Lambda3^x6)/x6!", "description": "<p>And</p>", "templateType": "anything"}, "x6": {"name": "x6", "group": "Question 1a", "definition": "random(3 .. 4#1)", "description": "", "templateType": "randrange"}, "hrs": {"name": "hrs", "group": "Question 2a(i)", "definition": "mins/60", "description": "", "templateType": "anything"}, "x9": {"name": "x9", "group": "Question 1b", "definition": "4", "description": "", "templateType": "number"}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": [], "variable_groups": [{"name": "Question 2a(i)", "variables": ["x1", "hrs", "mins", "Ans1", "rate", "Lambda1", "xx1", "Ansxx", "rate2"]}, {"name": "Question 2a(ii)", "variables": ["Ans2", "x2"]}, {"name": "Question 2b", "variables": ["Timemins", "Timeminsno", "Timehrs", "Daypart", "Totaltime", "Lambda2", "Ans3", "Hours", "x3", "Totalmins", "Ans4"]}, {"name": "Question 1a", "variables": ["Ans5", "Ans6", "Ans7", "Lambda3", "x4", "x5", "x6", "x7"]}, {"name": "Question 1b", "variables": ["Lambda4", "x8", "x9", "x10", "x11", "Ans8", "Ans9", "Ans10", "Ans11"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Question 1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>(a) Given that&nbsp; $X\\sim Po\\left({\\var{Lambda3}}\\right)$. Find,</p>\n<p>(i) $P\\left(X=\\var{x5}\\right)$</p>\n<p>Answer:[[0]]</p>\n<p></p>\n<p>(ii) $P\\left(X=\\var{x6}\\right)$</p>\n<p>Answer:[[1]]</p>\n<p></p>\n<p>(iii) $P\\left(X=\\var{x7}\\right)$</p>\n<p>Answer:[[2]]</p>\n<p></p>\n<p>(b)&nbsp;Given that&nbsp; $X\\sim Po\\left({\\var{Lambda4}}\\right)$. Find,</p>\n<p>(i) $P(X&lt;\\var{x8})$&nbsp;</p>\n<p>Answer:[[3]]</p>\n<p></p>\n<p>(ii) $P(X\\le\\var{x9})$</p>\n<p>Answer:[[4]]</p>\n<p></p>\n<p>(iii) $P(X&gt;\\var{x10})$</p>\n<p>Answer:[[5]]</p>\n<p></p>\n<p>(iv) $P(X\\ge\\var{x11})$</p>\n<p>Answer:[[6]]</p>\n<p></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": "{Ans5}", "maxValue": "{Ans5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{Ans6}", "maxValue": "{Ans6}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{Ans7}", "maxValue": "{Ans7}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": 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, "minValue": "{Ans8}", "maxValue": "{Ans8}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": 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, "minValue": "{Ans9}", "maxValue": "{Ans9}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": 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, "minValue": "{Ans10}", "maxValue": "{Ans10}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": 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, "minValue": "{Ans11}", "maxValue": "{Ans11}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 2", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>(a)&nbsp;Patients arrive at a hospital A &amp; E department at random at a rate of {rate2} per hour.&nbsp;&nbsp;</p>\n<p>Let x be the r.v of the number of patients arriving per hour.&nbsp;</p>\n<p>Find the probability that, during any&nbsp;hour period, the number of patients arriving at the hospital accident and emergency department is</p>\n<p>(i) exactly {xx1}</p>\n<p>Answer:&nbsp;[[4]]</p>\n<p></p>\n<p>(b) Patients arrive at a hospital A &amp; E department at random at a rate of {rate} per hour.&nbsp;&nbsp;</p>\n<p>Let x be the r.v of the number of patients arriving per {mins} mins.&nbsp;</p>\n<p>Find the probability that, during any {mins} minute period, the number of patients arriving at the hospital accident and emergency department is</p>\n<p>(i) exactly {x1}&nbsp;</p>\n<p>Answer:&nbsp;[[0]]</p>\n<p>(ii) at least {x2}</p>\n<p>Answer:&nbsp;[[1]]</p>\n<p></p>\n<p>(c)&nbsp;A patient arrives at 11.00am. To find the probability that the next patient arrives before {Timehrs}.{Timemins}{Daypart}, x needs to be redefined.</p>\n<p>(i) Redefine the random variable x for part b by completing the below statement.&nbsp;</p>\n<p>Let x be the r.v of the number of patients arriving per&nbsp;[[2]]&nbsp;mins.&nbsp;</p>\n<p>(ii) Now find the probability that the next patient arrives before {Timehrs}.{Timemins}{Daypart}.</p>\n<p>Answer: [[3]]</p>\n<p></p>\n<p></p>", "gaps": [{"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, "minValue": "{Ans1}", "maxValue": "{Ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": 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": "{Ans2}", "maxValue": "{Ans2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{Ans3}", "maxValue": "{Ans3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "{Ans4}", "maxValue": "{Ans4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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"}, {"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, "minValue": "{Ansxx}", "maxValue": "{Ansxx}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Brad Allison", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3394/"}]}]}], "contributors": [{"name": "Brad Allison", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3394/"}]}