// Numbas version: exam_results_page_options
{"name": "Simon's copy of Clodagh's copy of 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": [{"variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "s", "zupper", "p", "amount", "p2", "tol", "zlower", "stuff", "prob2", "prob3", "prob1"], "variables": {"zlower": {"templateType": "anything", "group": "Ungrouped variables", "name": "zlower", "definition": "precround((m-lower)/s,2)", "description": ""}, "upper": {"templateType": "anything", "group": "Ungrouped variables", "name": "upper", "definition": "random(m+0.5s..m+1.5*s#5)", "description": ""}, "zupper": {"templateType": "anything", "group": "Ungrouped variables", "name": "zupper", "definition": "precround((upper-m)/s,2)", "description": ""}, "m": {"templateType": "anything", "group": "Ungrouped variables", "name": "m", "definition": "random(750..1250#50)", "description": ""}, "lower": {"templateType": "anything", "group": "Ungrouped variables", "name": "lower", "definition": "random(m-1.5*s..m-0.5s#5)", "description": ""}, "prob2": {"templateType": "anything", "group": "Ungrouped variables", "name": "prob2", "definition": "precround(1-p1,2)", "description": ""}, "s": {"templateType": "anything", "group": "Ungrouped variables", "name": "s", "definition": "random(60..100#10)", "description": ""}, "p": {"templateType": "anything", "group": "Ungrouped variables", "name": "p", "definition": "precround(normalcdf(zlower,0,1),4)", "description": ""}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "name": "tol", "definition": "0.01", "description": ""}, "prob3": {"templateType": "anything", "group": "Ungrouped variables", "name": "prob3", "definition": "precround(p1-p2,2)", "description": ""}, "prob1": {"templateType": "anything", "group": "Ungrouped variables", "name": "prob1", "definition": "precround(1-p,2)", "description": ""}, "units1": {"templateType": "anything", "group": "Ungrouped variables", "name": "units1", "definition": "\"k Wh\"", "description": ""}, "stuff": {"templateType": "anything", "group": "Ungrouped variables", "name": "stuff", "definition": "\"a frozen foods warehouse each week in the summer months \"", "description": ""}, "p2": {"templateType": "anything", "group": "Ungrouped variables", "name": "p2", "definition": "1-p", "description": ""}, "amount": {"templateType": "anything", "group": "Ungrouped variables", "name": "amount", "definition": "\"electricity consumption\"", "description": ""}, "p1": {"templateType": "anything", "group": "Ungrouped variables", "name": "p1", "definition": "precround(normalcdf(zupper,0,1),4)", "description": ""}}, "name": "Simon's copy of Clodagh's copy of Calculate probabilities from a normal distribution", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>rebelmaths</p>\n<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>"}, "preamble": {"js": "", "css": ""}, "extensions": ["stats"], "tags": [], "statement": "<p>The {amount}, $X$, of {stuff} &nbsp;is normally distributed with mean {m}{units1} and standard deviation {s}{units1}.</p>\n<p>&nbsp;</p>", "parts": [{"customMarkingAlgorithm": "", "unitTests": [], "variableReplacements": [], "prompt": "<p>(i)</p>\n<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>(ii)</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>(iii)</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>", "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "allowFractions": false, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacements": [], "maxValue": "prob1", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "customMarkingAlgorithm": "", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "2", "scripts": {}, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "minValue": "prob1", "mustBeReduced": false}, {"showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "allowFractions": false, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacements": [], "maxValue": "prob2", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "customMarkingAlgorithm": "", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "2", "scripts": {}, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "minValue": "prob2", "mustBeReduced": false}, {"showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "allowFractions": false, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "marks": "2", "variableReplacements": [], "maxValue": "prob3", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "customMarkingAlgorithm": "", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "2", "scripts": {}, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "minValue": "prob3", "mustBeReduced": false}], "extendBaseMarkingAlgorithm": true, "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false}], "advice": "<p>(i)</p>\n<p>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>(ii)</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>(iii)</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>", "variable_groups": [], "functions": {}, "rulesets": {}, "type": "question", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}