// Numbas version: finer_feedback_settings
{"name": "nuExam08 - Normal Distribution", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "preamble": {"js": "", "css": ""}, "name": "nuExam08 - Normal Distribution", "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "s", "zupper", "p", "amount", "p2", "tol", "zlower", "stuff", "prob2", "prob3", "prob1"], "rulesets": {}, "extensions": ["stats"], "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>", "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>", "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"}, "variable_groups": [], "variables": {"prob1": {"description": "", "name": "prob1", "templateType": "anything", "definition": "precround(1-p,2)", "group": "Ungrouped variables"}, "amount": {"description": "", "name": "amount", "templateType": "anything", "definition": "\"electricity consumption\"", "group": "Ungrouped variables"}, "p1": {"description": "", "name": "p1", "templateType": "anything", "definition": "precround(normalcdf(zupper,0,1),4)", "group": "Ungrouped variables"}, "zupper": {"description": "", "name": "zupper", "templateType": "anything", "definition": "precround((upper-m)/s,2)", "group": "Ungrouped variables"}, "upper": {"description": "", "name": "upper", "templateType": "anything", "definition": "random(m+0.5s..m+1.5*s#10000)", "group": "Ungrouped variables"}, "m": {"description": "", "name": "m", "templateType": "anything", "definition": "random(30000..50000#2000)", "group": "Ungrouped variables"}, "zlower": {"description": "", "name": "zlower", "templateType": "anything", "definition": "precround((m-lower)/s,2)", "group": "Ungrouped variables"}, "lower": {"description": "", "name": "lower", "templateType": "anything", "definition": "random(m-1.5*s..m-0.5s#10000)", "group": "Ungrouped variables"}, "p": {"description": "", "name": "p", "templateType": "anything", "definition": "precround(normalcdf(zlower,0,1),4)", "group": "Ungrouped variables"}, "prob3": {"description": "", "name": "prob3", "templateType": "anything", "definition": "precround(p1-p2,2)", "group": "Ungrouped variables"}, "tol": {"description": "", "name": "tol", "templateType": "anything", "definition": "0.01", "group": "Ungrouped variables"}, "p2": {"description": "", "name": "p2", "templateType": "anything", "definition": "1-p", "group": "Ungrouped variables"}, "units1": {"description": "", "name": "units1", "templateType": "anything", "definition": "\"k Wh\"", "group": "Ungrouped variables"}, "s": {"description": "", "name": "s", "templateType": "anything", "definition": "random(5000..15000#1000)", "group": "Ungrouped variables"}, "stuff": {"description": "", "name": "stuff", "templateType": "anything", "definition": "\"a frozen foods warehouse each week in the summer months \"", "group": "Ungrouped variables"}, "prob2": {"description": "", "name": "prob2", "templateType": "anything", "definition": "precround(1-p1,2)", "group": "Ungrouped variables"}}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"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>", "gaps": [{"variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "maxValue": "prob2", "allowFractions": false, "minValue": "prob2", "customName": "", "mustBeReducedPC": 0, "mustBeReduced": false, "strictPrecision": false, "showPrecisionHint": true, "useCustomName": false, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "precision": "2", "correctAnswerStyle": "plain", "precisionPartialCredit": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "precisionType": "dp", 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