// Numbas version: exam_results_page_options
{"name": "normal_3", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"pass": {"name": "pass", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "({pass_rate}-{m1})/{sd}"}, "n": {"name": "n", "description": "", "templateType": "randrange", "group": "Ungrouped variables", "definition": "random(1..2.5#0.1)"}, "pfail": {"name": "pfail", "description": "<p>prob of failing</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "normalcdf(pass,0,1)"}, "pass_rate": {"name": "pass_rate", "description": "<p>passrate</p>", "templateType": "randrange", "group": "Ungrouped variables", "definition": "random(40..50#5)"}, "sd": {"name": "sd", "description": "", "templateType": "randrange", "group": "Ungrouped variables", "definition": "random(6..11#1)"}, "m1": {"name": "m1", "description": "", "templateType": "randrange", "group": "Ungrouped variables", "definition": "random(55..70#1)"}, "m2": {"name": "m2", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "{m1}+{n}*{sd}"}, "p1": {"name": "p1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "normalcdf({n},0,1)"}}, "variable_groups": [], "name": "normal_3", "preamble": {"css": "", "js": ""}, "statement": "<p>A large group of students took a test in Maths and the final grades have a mean of \\(\\var{m1}\\)% and a standard deviation of \\(\\var{sd}\\)%.&nbsp;</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "ungrouped_variables": ["m1", "sd", "n", "m2", "p1", "pass", "pfail", "pass_rate"], "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "gaps": [{"showFeedbackIcon": true, "minValue": "(1-{p1})*100", "variableReplacements": [], "correctAnswerStyle": "plain", "precisionType": "dp", "allowFractions": false, "precision": "1", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "mustBeReducedPC": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxValue": "(1-{p1})*100", "marks": 1, "precisionPartialCredit": 0, "type": "numberentry", "showPrecisionHint": false, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"]}], "showCorrectAnswer": true, "prompt": "<p>If we approximate the distribution of these grades by a normal distribution, what percentage of the students scored higher than \\(\\var{m2}\\)%?&nbsp;</p>\n<p>Give your answer correct to one decimal place.&nbsp; &nbsp; &nbsp;&nbsp;[[0]]%</p>", "scripts": {}}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "gaps": [{"showFeedbackIcon": true, "minValue": "100*{pfail}", "variableReplacements": [], "correctAnswerStyle": "plain", "precisionType": "dp", "allowFractions": false, "precision": "1", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "mustBeReducedPC": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxValue": "100*{pfail}", "marks": 1, "precisionPartialCredit": 0, "type": "numberentry", "showPrecisionHint": false, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"]}], "showCorrectAnswer": true, "prompt": "<p>If the pass mark is \\(\\var{pass_rate}\\)% what percentage of the students should fail&nbsp;the test? &nbsp;</p>\n<p>Give&nbsp;your answer correct to one decimal place. &nbsp; &nbsp; &nbsp;&nbsp;[[0]]%</p>", "scripts": {}}], "advice": "<p>\\(X\\)&nbsp;has a mean of \\(\\var{m1}\\)% and a standard deviation of \\(\\var{sd}\\)%.&nbsp;</p>\n<p>(a) &nbsp; &nbsp;Find the percentage of the students scored higher than \\(\\var{m2}\\)%</p>\n<p style=\"padding-left: 90px;\">\\(P(X&gt;\\var{m2})=P\\left(Z&gt;\\frac{\\var{m2}-\\var{m1}}{\\var{sd}}\\right)\\)</p>\n<p style=\"padding-left: 240px;\">\\(=P(Z&gt;\\var{n})\\)</p>\n<p style=\"padding-left: 240px;\">\\(=1-P(Z&lt;\\var{n})\\)</p>\n<p style=\"padding-left: 240px;\">\\(=1-\\var{p1}\\)</p>\n<p style=\"padding-left: 240px;\">\\(=\\simplify{1-{p1}}\\)</p>\n<p style=\"padding-left: 30px;\">The percentage of the students scored higher than \\(\\var{m2}\\)% in the exam&nbsp; = &nbsp;\\(\\simplify{100*(1-{p1})}\\)%</p>\n<p style=\"padding-left: 30px;\"></p>\n<p>(b) &nbsp; \\(P(Failing)=P(X&lt;\\var{pass_rate})\\)</p>\n<p style=\"padding-left: 120px;\">&nbsp; \\(=P\\left(Z&lt;\\frac{\\var{pass_rate}-\\var{m1}}{\\var{sd}}\\right)\\)</p>\n<p style=\"padding-left: 120px;\">&nbsp; \\(=P(Z&lt;\\var{pass})\\)</p>\n<p style=\"padding-left: 120px;\">&nbsp; \\(=1-P(Z&lt;\\simplify{-{pass}})\\)</p>\n<p style=\"padding-left: 120px;\">&nbsp; \\(=1-\\simplify{1-{pfail}}\\)</p>\n<p style=\"padding-left: 120px;\">&nbsp; \\(=\\var{pfail}\\)</p>\n<p style=\"padding-left: 30px;\">The&nbsp;percentage of the students that should fail&nbsp;the test is thus \\(\\simplify{100*{pfail}}\\)%</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": ["stats"], "functions": {}, "rulesets": {}, "tags": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}