// Numbas version: exam_results_page_options
{"name": "MSS - Normal Distribution Area Mid", "extensions": ["stats", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MSS - Normal Distribution Area Mid", "tags": ["Normal distribution", "normal distribution", "statistics"], "metadata": {"description": "<p>Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The graph below displays a standard normal distribution.</p>", "advice": "<p>The rules of thumb for the normal distribution show that:</p>\n<ul>\n<li>the area between $-1$ and $+1$ standard deviations is approximately $68$%.</li>\n</ul>\n<ul>\n<li>the area between $-2$ and $+2$ standard deviations is approximately $95$%.</li>\n</ul>\n<ul>\n<li>the area between $-3$ and $+3$ standard deviations is approximately $99.7$%.</li>\n</ul>", "rulesets": {}, "extensions": ["jsxgraph", "stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"question_areapercentage": {"name": "question_areapercentage", "group": "Ungrouped variables", "definition": "random([68,95,99.7])", "description": "<p>P(-Z&lt;= z &lt;=Z)</p>", "templateType": "anything", "can_override": false}, "normdist_midproportion": {"name": "normdist_midproportion", "group": "Ungrouped variables", "definition": "jessiecode(700, 400, [-5, 0.7, 5, -0.2], \"snapslider={snapslider};\"+safe(\"\"\"\n  xaxis=axis([0,0],[1,0]) <<\n  ticks: <<majorHeight: 30, drawZero: true, label: <<offset: [-4,-25]>> >>,\n  name: 'z',\n  withLabel: true,\n  label: <<position: 'rt', offset: [-5,10]>>\n  >>;\n  \n  slider([0,0.55],[3,0.55],[0,0.5,6]) <<id: 'slider', name: 'Z', snapWidth: snapslider, withLabel: false>>;\n  \n  functiongraph(function(x){return 1/(sqrt(2*PI))*exp(-0.5*(x)^2);}, -8, 8) <<highlight: true, strokeWidth: 1>>;  \n  \n  drawnGaussian = functiongraph(function(x){return 1/(sqrt(2*PI))*exp(-0.5*(x)^2);}, function(){return -Z.Value();} , function(){return Z.Value();}) <<highlight: true, strokeWidth: 3>>;\n  \n  drawnGaussianShaded = inequality(drawnGaussian) <<visible: false>>;\n    \n  invisibleBox = polygon([-7,-0.001],[7,-0.001],[8,1],[-8,1]) <<visible: false, hasInnerPoints: false>>;\n    \n  ci = curveintersection(invisibleBox, drawnGaussianShaded) <<visible: true, inverse: true, fillColor: 'green', fillOpacity: 0.3>>;\n    \n  \"\"\"),\n[\"axis\": false,\n \"showNavigation\": false,\n \"grid\": false,\n \"showCopyright\": false,\n \"keepaspectratio\": false  \n  ])", "description": "", "templateType": "anything", "can_override": false}, "question_zscore": {"name": "question_zscore", "group": "Ungrouped variables", "definition": "normalinv((question_areapercentage*0.01+1)/2, 0, 1)", "description": "", "templateType": "anything", "can_override": false}, "snapslider": {"name": "snapslider", "group": "Ungrouped variables", "definition": "0.5", "description": "", "templateType": "number", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["question_areapercentage", "normdist_midproportion", "question_zscore", "snapslider"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "pos:\n  jxg_value(normdist_midproportion[\"slider\"])\n\nstudentZScore:\n  withintolerance(pos,question_zscore,snapslider/2)\n\nstudent_feedback:\n   feedback(\"You selected a z-score of \" + pos + \". The probability of randomly selecting a value between \" +\n  \"$-z$ and $z$ is approximately \" + precround((1-(1-normalcdf(pos,0,1))*2)*100,1) + \"%.\")\n\nmark:\n  correctif(studentZScore);\n  apply(student_feedback)\n\ninterpreted_answer:\n  pos", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Adjust the slider so that the shaded area under the curve is equal to approximately $\\var{question_areapercentage}$% of the total area under the curve.</p>\n<p>{normdist_midproportion}</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Jim Pettigrew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2037/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"name": "Brent Le Cornu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18260/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Jim Pettigrew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2037/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"name": "Brent Le Cornu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18260/"}]}