// Numbas version: finer_feedback_settings
{"name": "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": [{"tags": ["ACC1012", "checked2015", "MAS1403"], "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>", "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "gaps": [{"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 1, "minValue": "prob1-tol", "maxValue": "prob1+tol", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 1, "minValue": "prob2-tol", "maxValue": "prob2+tol", "allowFractions": false, "correctAnswerFraction": false}]}], "preamble": {"js": "", "css": ""}, "functions": {}, "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>", "metadata": {"description": "<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>", "notes": "\n    \t\t<p><strong>1/1/2012:</strong></p>\n    \t\t    <p>Can be configured to other applications using the string variables suppplied. Included tag sc.</p>\n    \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "\n  <p>The {amount}, $X$, of {stuff} &nbsp;is normally distributed with mean {m}k and standard deviation {s}{units1}.</p>\n  <p>i.e. &nbsp; \\[X \\sim \\operatorname{N}(\\var{m},\\var{s}^2)\\]</p>\n  <p>&nbsp;</p>\n  ", "rulesets": {}, "name": "Calculate probabilities from normal distribution,", "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "showQuestionGroupNames": false, "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "amount", "zupper", "p", "s", "stuff", "tol", "zlower", "prob2", "prob1"], "variables": {"tol": {"name": "tol", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "0.01"}, "lower": {"name": "lower", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(m-1.5*s..m-0.5s#5)"}, "prob2": {"name": "prob2", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(1-p1,2)"}, "zupper": {"name": "zupper", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround((upper-m)/s,2)"}, "zlower": {"name": "zlower", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround((m-lower)/s,2)"}, "m": {"name": "m", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(750..1250#50)"}, "p1": {"name": "p1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(normalcdf(zupper,0,1),4)"}, "amount": {"name": "amount", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "\"electricity consumption\""}, "upper": {"name": "upper", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(m+0.5s..m+1.5*s#5)"}, "stuff": {"name": "stuff", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "\"a frozen foods warehouse each week in the summer months \""}, "s": {"name": "s", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(60..100#10)"}, "units1": {"name": "units1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "\"k Wh\""}, "prob1": {"name": "prob1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(1-p,2)"}, "p": {"name": "p", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(normalcdf(zlower,0,1),4)"}}, "variable_groups": [], "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}