// Numbas version: exam_results_page_options
{"name": "Julie'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": [{"name": "Julie's copy of Clodagh's copy of Calculate probabilities from a normal distribution", "tags": [], "metadata": {"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>", "licence": "Creative Commons Attribution 4.0 International"}, "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>", "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>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"lower": {"name": "lower", "group": "Ungrouped variables", "definition": "random(m-1.5*s..m-0.5s#5)", "description": "", "templateType": "anything", "can_override": false}, "upper": {"name": "upper", "group": "Ungrouped variables", "definition": "random(m+0.5s..m+1.5*s#5)", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.01", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "precround(normalcdf(zlower,0,1),4)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(750..1250#50)", "description": "", "templateType": "anything", "can_override": false}, "zupper": {"name": "zupper", "group": "Ungrouped variables", "definition": "precround((upper-m)/s,2)", "description": "", "templateType": "anything", "can_override": false}, "p1": {"name": "p1", "group": "Ungrouped variables", "definition": "precround(normalcdf(zupper,0,1),4)", "description": "", "templateType": "anything", "can_override": false}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "1-p", "description": "", "templateType": "anything", "can_override": false}, "prob1": {"name": "prob1", "group": "Ungrouped variables", "definition": "precround(1-p,2)", "description": "", "templateType": "anything", "can_override": false}, "zlower": {"name": "zlower", "group": "Ungrouped variables", "definition": "precround((m-lower)/s,2)", "description": "", "templateType": "anything", "can_override": false}, "prob2": {"name": "prob2", "group": "Ungrouped variables", "definition": "precround(1-p1,2)", "description": "", "templateType": "anything", "can_override": false}, "amount": {"name": "amount", "group": "Ungrouped variables", "definition": "\"electricity consumption\"", "description": "", "templateType": "anything", "can_override": false}, "units1": {"name": "units1", "group": "Ungrouped variables", "definition": "\"k Wh\"", "description": "", "templateType": "anything", "can_override": false}, "stuff": {"name": "stuff", "group": "Ungrouped variables", "definition": "\"a frozen foods warehouse each week in the summer months \"", "description": "", "templateType": "anything", "can_override": false}, "prob3": {"name": "prob3", "group": "Ungrouped variables", "definition": "precround(p1-p2,2)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "random(60..100#10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["units1", "upper", "lower", "p1", "m", "s", "zupper", "p", "amount", "p2", "tol", "zlower", "stuff", "prob2", "prob3", "prob1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "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></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "prob1-tol", "maxValue": "prob1+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the probability that in a particular week the {amount} is greater than {upper} {units1}:</p>\n<p>Probability = ?[[0]](to 2 &nbsp;decimal places)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "prob2-tol", "maxValue": "prob2+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the probability that in a particular week the {amount} is between {lower}{units1} and {upper} {units1}:</p>\n<p>Probability = ?[[0]](to 2 &nbsp;decimal places)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "prob3-tol", "maxValue": "prob3+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}