// Numbas version: exam_results_page_options
{"name": "Julie's copy of Clodagh's copy of Julie's copy of Calculate probabilities from normal distribution, ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>rebelmaths</p>\n<p>Given a random variable $X$ 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>"}, "tags": ["ACC1012", "checked2015", "MAS1403", "rebelmaths"], "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "amount", "zupper", "p", "s", "stuff", "tol", "zlower", "prob2", "prob1"], "functions": {}, "variable_groups": [], "showQuestionGroupNames": false, "parts": [{"prompt": "<p>Find the probability that in a particular week the {amount} is less than {lower} {units1}:</p>\n<p>Probability = ?[[0]](to 2 &nbsp;decimal places)</p>\n<p>Find the probability that in a particular week the {amount} is greater than {upper} {units1}:</p>\n<p>Probability = ?[[1]](to 2 &nbsp;decimal places)</p>", "variableReplacements": [], "marks": 0, "type": "gapfill", "gaps": [{"allowFractions": false, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "prob1+tol", "variableReplacements": [], "scripts": {}, "minValue": "prob1-tol", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "marks": 1}, {"allowFractions": false, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "prob2+tol", "variableReplacements": [], "scripts": {}, "minValue": "prob2-tol", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "marks": 1}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "extensions": ["stats"], "advice": "<p>1. Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &lt; {lower}) = P(Z &lt; ({lower} -{m}) / {s}) =1 -P(Z &lt; {m-lower}/{s})} = 1-P(z&lt;\\var{zlower})=1 -\\var{p} = \\var{prob1}$ to 2 decimal places.</p>\n<p>2. Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &gt; {upper}) = P(Z &gt; ({upper} -{m}) / {s}) = 1 -P(Z &lt; {upper-m}/{s})} = 1-P(z&lt;\\var{zupper})=1-\\var{p1} = \\var{prob2}$ to 2 decimal places.</p>", "name": "Julie's copy of Clodagh's copy of Julie's copy of Calculate probabilities from normal distribution, ", "statement": "<p>The {amount}, $X$, of {stuff} &nbsp;is normally distributed with mean {m}k Wh and standard deviation {s}{units1}.</p>\n<p></p>\n<p>&nbsp;</p>", "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "variables": {"zupper": {"definition": "precround((upper-m)/s,2)", "name": "zupper", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "amount": {"definition": "\"electricity consumption\"", "name": "amount", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "units1": {"definition": "\"k Wh\"", "name": "units1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "tol": {"definition": "0.01", "name": "tol", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "s": {"definition": "random(60..100#10)", "name": "s", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"definition": "random(750..1250#50)", "name": "m", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prob1": {"definition": "precround(1-p,2)", "name": "prob1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prob2": {"definition": "precround(1-p1,2)", "name": "prob2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "upper": {"definition": "random(m+0.5s..m+1.5*s#5)", "name": "upper", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "lower": {"definition": "random(m-1.5*s..m-0.5s#5)", "name": "lower", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "stuff": {"definition": "\"a frozen foods warehouse each week in the summer months \"", "name": "stuff", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "zlower": {"definition": "precround((m-lower)/s,2)", "name": "zlower", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"definition": "precround(normalcdf(zupper,0,1),4)", "name": "p1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "p": {"definition": "precround(normalcdf(zlower,0,1),4)", "name": "p", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}