// 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": [{"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>", "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"}, "parts": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}, "marks": 0, "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "marks": "1", "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "customName": "", "precisionType": "dp", "showCorrectAnswer": true, "maxValue": "prob2", "minValue": "prob2", "precision": "2", "strictPrecision": false, "precisionPartialCredit": 0, "mustBeReduced": false, "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true}], "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "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>", "sortAnswers": false}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}, "marks": 0, "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "marks": "2", "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "customName": "", "precisionType": "dp", "showCorrectAnswer": true, "maxValue": "prob3", "minValue": "prob3", "precision": "2", "strictPrecision": false, "precisionPartialCredit": 0, "mustBeReduced": false, "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true}], "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "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>", "sortAnswers": false}], "tags": [], "variable_groups": [], "extensions": ["stats"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Brad's copy of nuExam08 - Normal Distribution", "ungrouped_variables": ["lower", "m", "zlower", "s"], "variables": {"s": {"definition": "1", "group": "Ungrouped variables", "name": "s", "templateType": "anything", "description": ""}, "zlower": {"definition": "precround((m-lower)/s,2)", "group": "Ungrouped variables", "name": "zlower", "templateType": "anything", "description": ""}, "m": {"definition": "random(30000..50000#2000)", "group": "Ungrouped variables", "name": "m", "templateType": "anything", "description": ""}, "lower": {"definition": "random(m-1.5*s..m-0.5s#10000)", "group": "Ungrouped variables", "name": "lower", "templateType": "anything", "description": ""}}, "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": ""}, "functions": {}, "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/"}]}