// Numbas version: exam_results_page_options
{"name": "Michael's copy of Practice using the Normal Distribution Tables", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["z1", "z2", "z3", "z4", "z5", "z6", "z7", "z8", "p1", "p2", "p3", "p4", "p5", "p6", "tol", "prob1", "zval1", "tol2", "prob2", "zval2", "percentage", "xlow", "mean_b", "sdev_b", "xhigh"], "variables": {"tol": {"name": "tol", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "0.001"}, "xlow": {"name": "xlow", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalinv(0.5-(percentage/200),mean_b,sdev_b)"}, "z1": {"name": "z1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.2..2#0.01)"}, "sdev_b": {"name": "sdev_b", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(6..20#2)"}, "z3": {"name": "z3", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-2..-0.2#0.01)"}, "z7": {"name": "z7", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-2..-0.2#0.01)"}, "prob1": {"name": "prob1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.02..0.3#0.01)"}, "z6": {"name": "z6", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..2#0.01)"}, "z5": {"name": "z5", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.2..0.9#0.01)"}, "p3": {"name": "p3", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalcdf(z3,0,1)"}, "z2": {"name": "z2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.2..2#0.01)"}, "zval2": {"name": "zval2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "-normalinv(prob2, 0,1)"}, "z4": {"name": "z4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-2..-0.2#0.01)"}, "z8": {"name": "z8", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.2..2#0.01)"}, "p5": {"name": "p5", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalcdf(z6,0,1)-normalcdf(z5,0,1)"}, "prob2": {"name": "prob2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0.02..0.4#0.01)"}, "zval1": {"name": "zval1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalinv(prob1,0,1)"}, "p4": {"name": "p4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "1-normalcdf(z4,0,1)"}, "percentage": {"name": "percentage", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(95,90,80)"}, "tol2": {"name": "tol2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "0.01"}, "p1": {"name": "p1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalcdf(z1,0,1)"}, "p6": {"name": "p6", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalcdf(z8,0,1)-normalcdf(z7,0,1)"}, "xhigh": {"name": "xhigh", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalinv(0.5+percentage/200,mean_b,sdev_b)"}, "mean_b": {"name": "mean_b", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(100..200#10)"}, "p2": {"name": "p2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "1-normalcdf(z2,0,1)"}}, "functions": {}, "name": "Michael's copy of Practice using the Normal Distribution Tables", "parts": [{"marks": 0, "unitTests": [], "scripts": {}, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p1-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p1+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p2-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p2+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p3-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p3+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p4-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p4+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p5-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p5+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "p6-tol", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "3", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "p6+tol", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}], "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p>$P(Z &lt; \\var{z1}) =$&nbsp;[[0]]&nbsp; &nbsp;</p>\n<p>$P(Z &gt;\\var{z2}) =$&nbsp;[[1]]</p>\n<p>$P(Z &lt;\\var{z3}) =$&nbsp;[[2]]</p>\n<p>$P(Z &gt;\\var{z4}) =$&nbsp;[[3]]</p>\n<p>$P(\\var{z5} &lt; Z &lt;\\var{z6})$ =&nbsp; [[4]]</p>\n<p>$P(\\var{z7} &lt; Z &lt;\\var{z8})$ = [[5]]</p>", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true}, {"marks": 0, "unitTests": [], "scripts": {}, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "zval1-tol2", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "zval1+tol2", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "variableReplacements": [], "marks": 1, "precisionPartialCredit": 0, "scripts": {}, "minValue": "zval2-tol2", "mustBeReduced": false, "allowFractions": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showFeedbackIcon": true, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "maxValue": "zval2+tol2", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "showPrecisionHint": true}, {"correctAnswerStyle": "plain", "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "marks": 1, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "xlow+0.5", "customMarkingAlgorithm": "", "minValue": "xlow-0.5", "mustBeReduced": false, "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerFraction": false}, {"correctAnswerStyle": "plain", "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "marks": 1, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "xhigh+0.5", "customMarkingAlgorithm": "", "minValue": "xhigh-0.5", "mustBeReduced": false, "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerFraction": false}], "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p>Find the value of $z1$ where $P(Z&lt;z1) = \\var{prob1}$</p>\n<p>$z1 =$&nbsp;&nbsp;[[0]]</p>\n<p>Find the value of $z2$ where $P(Z&gt;z2) = \\var{prob2}$</p>\n<p></p>\n<p>$z2 = $[[1]]</p>\n<p>What are the values of X<sub>low</sub>&nbsp;and X<sub>high</sub> which between them contain the central $\\var{percentage}$ % of values in a normal distribution, with mean&nbsp;$\\var{mean_b}$ and standard deviation of $\\var{sdev_b}$.</p>\n<p>X<sub>low =[[2]]</sub></p>\n<p>X<sub>high =[[3]]</sub></p>", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true}], "tags": [], "statement": "<p>Use the Standard Normal Distribution Tables&nbsp;to answer the questions below.</p>\n<p></p>", "preamble": {"css": "", "js": ""}, "extensions": ["stats"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p></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>"}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}