// Numbas version: exam_results_page_options
{"name": "IP3.1", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["strexceed", "idef", "period", "episodes", "rdexp", "u2", "check", "n9", "u1", "u3", "probexceed", "ecom", "d", "p2", "p3", "p0", "p1", "p6", "p7", "p4", "p5", "p8", "t2", "t1", "n8", "thing", "s", "r", "t", "activity", "n1", "n2", "n3", "n4", "n5", "n6", "n7"], "name": "IP3.1", "tags": ["PMF", "Probability", "discrete distribution", "expectation", "expected value", "mass function", "pmf", "probability", "probability mass function", "query", "sc", "statistics", "tested1"], "preamble": {"css": "", "js": ""}, "advice": "<h4>a)</h4>\n<p>The expected number is given by:</p>\n<p>\\[\\simplify[]{{p0 / 100} * {n1} + {p1 / 100} * {n2} + {p2 / 100} * {n3} + {p3 / 100} * {n4} + {p4 / 100} * {n5} + {p5 / 100} * {n6} + {p6 / 100} * {n7} + {p7 / 100} * {n8} + {p8 / 100} * {n9} = {ecom}}\\]</p>\n<h4>b)</h4>\n<p>We want the probability that the number of {episodes} exceeds $\\var{ecom}$</p>\n<p>This is the probability that the number exceeds $\\var{rdexp}$ and is</p>\n<p>\\[\\sum_{i=\\var{rdexp+1}}^{i=8}\\left( \\mbox{Probability complaints}=i\\right)=\\simplify[]{{strexceed} }= \\var{probexceed/100}\\]</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>Find the expected number of {episodes} per {period}.</p>\n<p>Answer to $2$ decimal places</p>\n<p>Expected number = [[0]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 2, "maxValue": "{ecom+0.01}", "minValue": "{ecom-0.01}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>What is the probability that the number of {episodes} will exceed the expected number?</p>\n<p>Answer to $2$ decimal places.</p>\n<p>Probability = [[0]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 2, "maxValue": "{probexceed/100+0.01}", "minValue": "{probexceed/100-0.01}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "\n  <p>The probabilities that {idef} {thing} will receive {episodes} per {period} about its {activity} are given by the following table:</p>\n  <table border=\"3\">\n  <tbody>\n  <tr>\n  <td align=\"left\"><strong>Complaints</strong></td>\n  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th></tr>\n  <tr>\n  <td align=\"left\"><strong>Probability</strong></td>\n  <td>$\\var{p0/100}$</td>\n  <td>$\\var{p1/100}$</td>\n  <td>$\\var{p2/100}$</td>\n  <td>$\\var{p3/100}$</td>\n  <td>$\\var{p4/100}$</td>\n  <td>$\\var{p5/100}$</td>\n  <td>$\\var{p6/100}$</td>\n  <td>$\\var{p7/100}$</td>\n  <td>$\\var{p8/100}$</td>\n  </tr>\n  </tbody>\n  </table>\n  <p>Answer the following two parts:</p>\n  ", "type": "question", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"strexceed": {"definition": "if(ecom>3,p4/100+'+'+p5/100+'+'+p6/100+'+'+p7/100+'+'+p8/100,if(ecom>4,p5/100+'+'+p6/100+'+'+p7/100+'+'+p8/100,if(ecom>5,p6/100+'+'+p7/100+'+'+p8/100,p3/100+'+'+p4/100+'+'+p5/100+'+'+p6/100+'+'+p7/100+'+'+p8/100)))", "templateType": "anything", "group": "Ungrouped variables", "name": "strexceed", "description": ""}, "idef": {"definition": "'an'", "templateType": "anything", "group": "Ungrouped variables", "name": "idef", "description": ""}, "period": {"definition": "'day'", "templateType": "anything", "group": "Ungrouped variables", "name": "period", "description": ""}, "episodes": {"definition": "'complaints'", "templateType": "anything", "group": "Ungrouped variables", "name": "episodes", "description": ""}, "rdexp": {"definition": "floor(ecom)", "templateType": "anything", "group": "Ungrouped variables", "name": "rdexp", "description": ""}, "probexceed": {"definition": "if(ecom>3,p4+p5+p6+p7+p8,if(ecom>4,p5+p6+p7+p8,if(ecom>5,p6+p7+p8,100-p0-p1-p2)))", "templateType": "anything", "group": "Ungrouped variables", "name": "probexceed", "description": ""}, "check": {"definition": "p0+p1+p2+p3+p4+p5+p6+p7+p8", "templateType": "anything", "group": "Ungrouped variables", "name": "check", "description": ""}, "thing": {"definition": "'airline'", "templateType": "anything", "group": "Ungrouped variables", "name": "thing", "description": ""}, "u1": {"definition": "round(d*random(70..100)/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "u1", "description": ""}, "u3": {"definition": "u1", "templateType": "anything", "group": "Ungrouped variables", "name": "u3", "description": ""}, "u2": {"definition": "u1", "templateType": "anything", "group": "Ungrouped variables", "name": "u2", "description": ""}, "ecom": {"definition": "(n1*p0+n2*p1+n3*p2+n4*p3+n5*p4+n6*p5+n7*p6+n8*p7+n9*p8)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "ecom", "description": ""}, "p7": {"definition": "p8+u1", "templateType": "anything", "group": "Ungrouped variables", "name": "p7", "description": ""}, "p2": {"definition": "p1+t2", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "r-p0-p1-p2", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "p0": {"definition": "s", "templateType": "anything", "group": "Ungrouped variables", "name": "p0", "description": ""}, "p1": {"definition": "p0+t1", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "p6": {"definition": "p7+u2", "templateType": "anything", "group": "Ungrouped variables", "name": "p6", "description": ""}, "d": {"definition": "round(t/15)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "p4": {"definition": "t-p8-p7-p6-p5", "templateType": "anything", "group": "Ungrouped variables", "name": "p4", "description": ""}, "p5": {"definition": "p6+u3", "templateType": "anything", "group": "Ungrouped variables", "name": "p5", "description": ""}, "p8": {"definition": "d", "templateType": "anything", "group": "Ungrouped variables", "name": "p8", "description": ""}, "t2": {"definition": "t1", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "t1": {"definition": "round(s*random(70..100)/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "n8": {"definition": "7", "templateType": "anything", "group": "Ungrouped variables", "name": "n8", "description": ""}, "n9": {"definition": "8", "templateType": "anything", "group": "Ungrouped variables", "name": "n9", "description": ""}, "s": {"definition": "round(r/10)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(45..65)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "t": {"definition": "100-r", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "activity": {"definition": "'luggage handling'", "templateType": "anything", "group": "Ungrouped variables", "name": "activity", "description": ""}, "n1": {"definition": "0", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "2", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "3", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "n5": {"definition": "4", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}, "n6": {"definition": "5", "templateType": "anything", "group": "Ungrouped variables", "name": "n6", "description": ""}, "n7": {"definition": "6", "templateType": "anything", "group": "Ungrouped variables", "name": "n7", "description": ""}}, "metadata": {"notes": "\n            \t\t<p><strong>7/07/2012:</strong></p>\n            \t\t        <p>Added tags.</p>\n            \t\t        <p>Checked calculation.</p>\n            \t\t        <p><strong>22/07/2012:</strong></p>\n            \t\t        <p>Added description.</p>\n            \t\t        <p>Ticked stats extension box.</p>\n            \t\t        <p><strong>31/07/2012:</strong></p>\n            \t\t        <p>Added tags.</p>\n            \t\t        <p>Question appears to be working correctly.</p>\n            \t\t        <p><strong>20/12/2012:</strong></p>\n            \t\t        <p>Could increase the number of scenarios by using random string variables. Query tag added for that.</p>\n            \t\t        <p>Also very cumbersome use of variables. But no change proposed for now.</p>\n            \t\t        <p>Checked calculation, OK. Added tested1 tag.</p>\n            \t\t        <p><strong>21/12/2012:</strong></p>\n            \t\t        <p>Although asks for solution to 2 dps, there is no rounding as the raw values are to 2 dps. Added sc tag for possible scenarios.</p>\n            \t\t", "description": "<p>Given a probability mass function $P(X=i)$ with outcomes $i \\in \\{0,1,2,\\ldots 8\\}$, find the expectation $E$ and $P(X \\gt E)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}