// Numbas version: finer_feedback_settings
{"name": "normal_3", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "normal_3", "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>", "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>", "extensions": ["stats"], "type": "question", "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "variables": {"p1": {"name": "p1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "normalcdf({n},0,1)"}, "m1": {"name": "m1", "templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(55..70#1)"}, "pfail": {"name": "pfail", "templateType": "anything", "description": "<p>prob of failing</p>", "group": "Ungrouped variables", "definition": "normalcdf(pass,0,1)"}, "n": {"name": "n", "templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(1..2.5#0.1)"}, "pass_rate": {"name": "pass_rate", "templateType": "randrange", "description": "<p>passrate</p>", "group": "Ungrouped variables", "definition": "random(40..50#5)"}, "sd": {"name": "sd", "templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(6..11#1)"}, "m2": {"name": "m2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "{m1}+{n}*{sd}"}, "pass": {"name": "pass", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "({pass_rate}-{m1})/{sd}"}}, "tags": [], "parts": [{"variableReplacements": [], "showFeedbackIcon": 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>", "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "gaps": [{"scripts": {}, "variableReplacements": [], "precisionPartialCredit": 0, "minValue": "(1-{p1})*100", "type": "numberentry", "maxValue": "(1-{p1})*100", "precision": "1", "mustBeReduced": false, "showPrecisionHint": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}], "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"variableReplacements": [], "showFeedbackIcon": 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>", "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "gaps": [{"scripts": {}, "variableReplacements": [], "precisionPartialCredit": 0, "minValue": "100*{pfail}", "type": "numberentry", "maxValue": "100*{pfail}", "precision": "1", "mustBeReduced": false, "showPrecisionHint": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}], "variableReplacementStrategy": "originalfirst", "scripts": {}}], "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["m1", "sd", "n", "m2", "p1", "pass", "pfail", "pass_rate"], "rulesets": {}, "functions": {}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}], "resources": []}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}