// Numbas version: exam_results_page_options
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Converting to $\\operatorname{N}(0,1)$</p>\n  <p>$\\simplify[all,!collectNumbers]{P(X &lt; {lower}) = P(Z &lt; ({lower} -{m}) / {s}) = P(Z &lt; {lower-m}/{s}) = 1 -P(Z &lt; {m-lower}/{s})} = 1 -\\var{p} = \\var{precround(1 -p,4)}$&nbsp;to 4 decimal places.</p>\n  <p>2. Converting to $\\operatorname{N}(0,1)$</p>\n  <p>$\\simplify[all,!collectNumbers]{P(X &gt; {upper}) = P(Z &gt; ({upper} -{m}) / {s}) = P(Z &gt; {upper-m}/{s}) = 1 -P(Z &lt; {upper-m}/{s})} = 1-\\var{p1} = \\var{precround(1 -p1,4)}$ to 4 decimal places.</p>\n    ", "rulesets": {}, "parts": [{"prompt": "<p>Find the probability that in a particular week the {amount} is less than {lower} {units1}:</p>\n<p>Probability = [[0]]&nbsp;(to 4 &nbsp;decimal places)</p>\n<p>Find the probability that in a particular week the {amount} is greater than {upper} {units1}:</p>\n<p>Probability = [[1]]&nbsp;(to 4 &nbsp;decimal places)</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "prob1+tol", "minValue": "prob1-tol", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "prob2+tol", "minValue": "prob2-tol", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "\n    <p>The {amount}, $X$, of {stuff} &nbsp;is normally distributed with mean {m}k and standard deviation {s}{units1}.</p>\n    <p>i.e. &nbsp; \\[X \\sim \\operatorname{N}(\\var{m},\\var{s}^2)\\]</p>\n    <p>&nbsp;</p>\n    ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"units1": {"definition": "\"k Wh\"", "templateType": "anything", "group": "Ungrouped variables", "name": "units1", "description": ""}, "upper": {"definition": "random(m+0.5s..m+1.5*s#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "upper", "description": ""}, "lower": {"definition": "random(m-1.5*s..m-0.5s#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "lower", "description": ""}, "p1": {"definition": "normalcdf((upper-m)/s,0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "m": {"definition": "random(750..1250#50)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "s": {"definition": "random(60..100#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "p": {"definition": "normalcdf((m-lower)/s,0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "amount": {"definition": "\"electricity consumption\"", "templateType": "anything", "group": "Ungrouped variables", "name": "amount", "description": ""}, "stuff": {"definition": "\"a frozen foods warehouse each week in the summer months \"", "templateType": "anything", "group": "Ungrouped variables", "name": "stuff", "description": ""}, "tol": {"definition": "0.0001", "templateType": "anything", "group": "Ungrouped variables", "name": "tol", "description": ""}, "prob2": {"definition": "precround(1-normalcdf(upper,m,s),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "prob2", "description": ""}, "prob1": {"definition": "precround(normalcdf(lower,m,s),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "prob1", "description": ""}}, "metadata": {"notes": "\n        \t\t<p><strong>1/1/2012:</strong></p>\n        \t\t    <p>Can be configured to other applications using the string variables suppplied. Included tag sc.</p>\n        \t\t", "description": "<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"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "navigation": {"reverse": true, "allowregen": true, "preventleave": false, "showfrontpage": false, "showresultspage": "oncompletion", "browse": true, "onleave": {"message": "", "action": "none"}}, "duration": 0, "showQuestionGroupNames": false, "timing": {"allowPause": true, "timeout": {"message": "", "action": "none"}, "timedwarning": {"message": "", "action": "none"}}, "feedback": {"showtotalmark": true, "allowrevealanswer": true, "showanswerstate": true, "showactualmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": []}, "metadata": {"description": "\n    \t\t<p>6 questions on standard statistical distributions.</p>\n    \t\t    <p>Binomial, Poisson, Normal, Uniform, Exponential.</p>\n    \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "name": "The normal distribution", "percentPass": 0, "showstudentname": true, "type": "exam", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Lauren Frances Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2490/"}, {"name": "Brad Allison", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3394/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}