// Numbas version: finer_feedback_settings
{"name": "Brad's copy of nuExam08 - Normal Distribution", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "parts": [{"customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "useCustomName": false, "type": "gapfill", "prompt": "<p>If one electrician is chosen at random, what is probability that this electrician earns over &pound;{upper}?&nbsp;</p>\n<p>Probability = [[0]](to 2 &nbsp;decimal places)</p>\n<p></p>", "scripts": {}, "customName": "", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"customMarkingAlgorithm": "", "marks": "1", "precisionType": "dp", "mustBeReduced": false, "precision": "2", "correctAnswerStyle": "plain", "scripts": {}, "precisionPartialCredit": 0, "minValue": "prob2", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "maxValue": "prob2", "mustBeReducedPC": 0, "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customName": "", "useCustomName": false, "extendBaseMarkingAlgorithm": true, "strictPrecision": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "unitTests": [], "variableReplacementStrategy": "originalfirst"}, {"customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "useCustomName": false, "type": "gapfill", "prompt": "<p>If one electrician is chosen at random, what is probability that this electrician earns&nbsp;between &pound;{lower} and &pound;{upper}?</p>\n<p>Probability = [[0]](to 2 &nbsp;decimal places)</p>", "scripts": {}, "customName": "", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"customMarkingAlgorithm": "", "marks": "2", "precisionType": "dp", "mustBeReduced": false, "precision": "2", "correctAnswerStyle": "plain", "scripts": {}, "precisionPartialCredit": 0, "minValue": "prob3", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "maxValue": "prob3", "mustBeReducedPC": 0, "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customName": "", "useCustomName": false, "extendBaseMarkingAlgorithm": true, "strictPrecision": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "variables": {"mu": {"definition": "3", "group": "Ungrouped variables", "templateType": "anything", "name": "mu", "description": ""}, "Z": {"definition": "precround((X-mu)/sd/sqrt(50),2)", "group": "Ungrouped variables", "templateType": "anything", "name": "Z", "description": ""}, "p1": {"definition": "normalcdf(Z,z,1)", "group": "Ungrouped variables", "templateType": "anything", "name": "p1", "description": "<p>precround(normalcdf(ZTeststat,0,1),4)</p>"}, "X": {"definition": "5.5", "group": "Ungrouped variables", "templateType": "anything", "name": "X", "description": "<p>random(mu+0.5sd..mu+1.5*sd#10000)</p>"}, "sd": {"definition": "5", "group": "Ungrouped variables", "templateType": "anything", "name": "sd", "description": ""}}, "tags": [], "extensions": ["stats"], "name": "Brad's copy of nuExam08 - Normal Distribution", "metadata": {"description": "<p>Given a random variable $X$ &nbsp;normally distributed as $\\operatorname{N}(m,\\sigma^2)$ find probabilities $P(X \\gt a),\\; a \\gt m;\\;\\;P(X \\lt b),\\;b \\lt m$.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "advice": "<p><strong>(a)</strong></p>\n<p>Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &gt; {upper}) = P(Z &gt; ({upper} -{m}) / {s})} = P(Z&gt;\\var{zupper}) = 1-P(Z&lt;\\var{zupper})=1-\\var{p1} = \\var{prob2}$ to 2 decimal places.</p>\n<p><strong></strong></p>\n<p><strong>(b)</strong></p>\n<p>$\\simplify[all,!collectNumbers]{P({lower} &lt; X &lt; {upper}) = P(X &lt; {upper})-P(X &lt; {lower})}=P(Z&lt;\\var{zupper})-P(Z&lt;-\\var{zlower}) =\\var{p1}-\\var{p2} = \\var{prob3}$ to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong></strong></p>", "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "statement": "<p>The salary of an electrician&nbsp;is normally distributed with mean &pound;{m} and standard deviation &pound;{s}.</p>\n<p>&nbsp;</p>", "ungrouped_variables": ["X", "p1", "mu", "sd", "Z"], "type": "question", "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": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Brad Allison", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3394/"}]}]}], "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": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Brad Allison", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3394/"}]}