// Numbas version: exam_results_page_options
{"name": "Calculate probabilities from a normal distribution", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.01", "description": "", "name": "tol"}, "amount": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"electricity consumption\"", "description": "", "name": "amount"}, "p1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(normalcdf(zupper,0,1),4)", "description": "", "name": "p1"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(750..1250#50)", "description": "", "name": "m"}, "prob3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(p1-p2,2)", "description": "", "name": "prob3"}, "prob1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(1-p,2)", "description": "", "name": "prob1"}, "zupper": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround((upper-m)/s,2)", "description": "", "name": "zupper"}, "stuff": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"a frozen foods warehouse each week in the summer months \"", "description": "", "name": "stuff"}, "lower": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(m-1.5*s..m-0.5s#5)", "description": "", "name": "lower"}, "p2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1-p", "description": "", "name": "p2"}, "zlower": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround((m-lower)/s,2)", "description": "", "name": "zlower"}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(60..100#10)", "description": "", "name": "s"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(normalcdf(zlower,0,1),4)", "description": "", "name": "p"}, "upper": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(m+0.5s..m+1.5*s#5)", "description": "", "name": "upper"}, "units1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"k Wh\"", "description": "", "name": "units1"}, "prob2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(1-p1,2)", "description": "", "name": "prob2"}}, "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "s", "zupper", "p", "amount", "p2", "tol", "zlower", "stuff", "prob2", "prob3", "prob1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Calculate probabilities from a normal distribution", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "prob1+tol", "minValue": "prob1-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "prob2+tol", "minValue": "prob2-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "prob3+tol", "minValue": "prob3-tol", "correctAnswerFraction": false, "marks": "2", "showPrecisionHint": false}], "type": "gapfill", "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>\n<p>Find the probability that in a particular week the {amount} is between {lower}{units1} and {upper} {units1}:</p>\n<p>Probability = ?[[2]](to 2 &nbsp;decimal places)</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>The {amount}, $X$, of {stuff} &nbsp;is normally distributed with mean {m}{units1} 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>", "tags": ["checked2015", "MAS1403"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>1/1/2012:</strong></p>\n<p>Can be configured to other applications using the string variables suppplied. Included tag sc.</p>\n<p><strong>26/11/2014:</strong></p>\n<p>Added an extra question on the probability that X lies between the upper and lower values. Edited the advice to reflect the use of tables in the module. </p>", "licence": "Creative Commons Attribution 4.0 International", "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>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>1. Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &lt; {lower}) = P(Z &lt; ({lower} -{m}) / {s})} = P(Z&lt;-\\var{zlower})= \\var{prob1}$ to 2 decimal places.</p>\n<p>2. Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &gt; {upper}) = P(Z &gt; ({upper} -{m}) / {s})} = P(Z&gt;\\var{zupper}) = 1-P(Z&lt;\\var{zupper})=1-\\var{p1} = \\var{prob2}$ to 2 decimal places.</p>\n<p>3. </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>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}