// Numbas version: finer_feedback_settings
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Converting to $\\operatorname{N}(0,1)$</p>\n<p>$\\simplify[all,!collectNumbers]{P(X &gt; {upper}) = P(Z &gt; ({upper} -{m}) / {s})} = P(Z&gt;\\var{zupper}) = 1-P(Z&lt;\\var{zupper})=1-\\var{p1} = \\var{prob2}$ to 2 decimal places.</p>\n<p>3. </p>\n<p>$\\simplify[all,!collectNumbers]{P({lower} &lt; X &lt; {upper}) = P(X &lt; {upper})-P(X &lt; {lower})}=P(Z&lt;\\var{zupper})-P(Z&lt;-\\var{zlower}) =\\var{p1}-\\var{p2} = \\var{prob3}$ to 2 decimal places.</p>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"lower": {"name": "lower", "group": "Ungrouped variables", "definition": "random(m-1.5*s..m-0.5s#5)", "description": "", "templateType": "anything", "can_override": false}, "upper": {"name": "upper", "group": "Ungrouped variables", "definition": "random(m+0.5s..m+1.5*s#5)", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", 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"precround(1-p,2)", "description": "", "templateType": "anything", "can_override": false}, "zlower": {"name": "zlower", "group": "Ungrouped variables", "definition": "precround((m-lower)/s,2)", "description": "", "templateType": "anything", "can_override": false}, "prob2": {"name": "prob2", "group": "Ungrouped variables", "definition": "precround(1-p1,2)", "description": "", "templateType": "anything", "can_override": false}, "amount": {"name": "amount", "group": "Ungrouped variables", "definition": "\"electricity consumption\"", "description": "", "templateType": "anything", "can_override": false}, "units1": {"name": "units1", "group": "Ungrouped variables", "definition": "\"k Wh\"", "description": "", "templateType": "anything", "can_override": false}, "stuff": {"name": "stuff", "group": "Ungrouped variables", "definition": "\"a frozen foods warehouse each week in the summer months \"", "description": "", "templateType": "anything", "can_override": false}, "prob3": {"name": "prob3", 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false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the probability that in a particular week the {amount} is between {lower}{units1} and {upper} {units1}:</p>\n<p>Probability = ?[[0]](to 2 &nbsp;decimal places)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, 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