// Numbas version: exam_results_page_options
{"name": "Probabilities from a normal distribution - Electrician", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "parts": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "prob2+tol", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "marks": "4", "mustBeReduced": false, "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "prob2-tol", "correctAnswerStyle": "plain", "correctAnswerFraction": false}], "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>", "showFeedbackIcon": true, "unitTests": [], "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "prob1+tol", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "marks": "4", "mustBeReduced": false, "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "prob1-tol", "correctAnswerStyle": "plain", "correctAnswerFraction": false}], "prompt": "<p>If one electrician is chosen at random, what is probability that this electrician earns less than &pound;{lower} ?</p>\n<p>Probability = [[0]](to 2 &nbsp;decimal places)</p>", "showFeedbackIcon": true, "unitTests": [], "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "prob3+tol", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "marks": "4", "mustBeReduced": false, "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "prob3-tol", "correctAnswerStyle": "plain", "correctAnswerFraction": false}], "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>", "showFeedbackIcon": true, "unitTests": [], "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false}], "functions": {}, "tags": [], "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "<p>1. 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>2.</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>", "variables": {"stuff": {"definition": "\"a frozen foods warehouse each week in the summer months \"", "templateType": "anything", "description": "", "name": "stuff", "group": "Ungrouped variables"}, "p1": {"definition": "precround(normalcdf(zupper,0,1),4)", "templateType": "anything", "description": "", "name": "p1", "group": "Ungrouped variables"}, "zupper": {"definition": "precround((upper-m)/s,2)", "templateType": "anything", "description": "", "name": "zupper", "group": "Ungrouped variables"}, "s": {"definition": "random(5000..15000#1000)", "templateType": "anything", "description": "", "name": "s", "group": "Ungrouped variables"}, "amount": {"definition": "\"electricity consumption\"", "templateType": "anything", "description": "", "name": "amount", "group": "Ungrouped variables"}, "prob2": {"definition": "precround(1-p1,2)", "templateType": "anything", "description": "", "name": "prob2", "group": "Ungrouped variables"}, "prob3": {"definition": "precround(p1-p2,2)", "templateType": "anything", "description": "", "name": "prob3", "group": "Ungrouped variables"}, "units1": {"definition": "\"k Wh\"", "templateType": "anything", "description": "", "name": "units1", "group": "Ungrouped variables"}, "tol": {"definition": "0.01", "templateType": "anything", "description": "", "name": "tol", "group": "Ungrouped variables"}, "zlower": {"definition": "precround((m-lower)/s,2)", "templateType": "anything", "description": "", "name": "zlower", "group": "Ungrouped variables"}, "lower": {"definition": "random(m-1.5*s..m-0.5s#10000)", "templateType": "anything", "description": "", "name": "lower", "group": "Ungrouped variables"}, "m": {"definition": "random(20000..40000#2000)", "templateType": "anything", "description": "", "name": "m", "group": "Ungrouped variables"}, "upper": {"definition": "random(m+0.5s..m+1.5*s#10000)", "templateType": "anything", "description": "", "name": "upper", "group": "Ungrouped variables"}, "prob1": {"definition": "precround(1-p,2)", "templateType": "anything", "description": "", "name": "prob1", "group": "Ungrouped variables"}, "p2": {"definition": "1-p", "templateType": "anything", "description": "", "name": "p2", "group": "Ungrouped variables"}, "p": {"definition": "precround(normalcdf(zlower,0,1),4)", "templateType": "anything", "description": "", "name": "p", "group": "Ungrouped variables"}}, "name": "Probabilities from a normal distribution - Electrician", "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>", "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "s", "zupper", "p", "amount", "p2", "tol", "zlower", "stuff", "prob2", "prob3", "prob1"], "variablesTest": {"condition": "", "maxRuns": 100}, "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"}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Ellen Marshall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2533/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Ellen Marshall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2533/"}]}