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$\\var{percentage}$ % of values in a normal distribution, with mean&nbsp;$\\var{mean_b}$ and standard deviation of $\\var{sdev_b}$.</p>\n<p>X<sub>low =[[2]]</sub></p>\n<p>X<sub>high =[[3]]</sub></p>", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "type": "gapfill", "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "showFeedbackIcon": true}], "functions": {}, "name": "Practise using the Normal Distribution Tables", "variables": {"z8": {"name": "z8", "definition": "random(0.2..2#0.01)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "tol2": {"name": "tol2", "definition": "0.01", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "z7": {"name": "z7", "definition": "random(-2..-0.2#0.01)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prob2": {"name": "prob2", "definition": "random(0.02..0.4#0.01)", 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"random(0.2..0.9#0.01)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"name": "p1", "definition": "normalcdf(z1,0,1)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "percentage": {"name": "percentage", "definition": "random(95,90,80)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "xhigh": {"name": "xhigh", "definition": "normalinv(0.5+percentage/200,mean_b,sdev_b)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "z1": {"name": "z1", "definition": "random(0.2..2#0.01)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "tol": {"name": "tol", "definition": "0.001", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "mean_b": {"name": "mean_b", "definition": "random(100..200#10)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "zval2": {"name": "zval2", 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{"name": "zval1", "definition": "normalinv(prob1,0,1)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p></p>\n<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>"}, "ungrouped_variables": ["z1", "z2", "z3", "z4", "z5", "z6", "z7", "z8", "p1", "p2", "p3", "p4", "p5", "p6", "tol", "prob1", "zval1", "tol2", "prob2", "zval2", "percentage", "xlow", "mean_b", "sdev_b", "xhigh"], "variable_groups": [], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": 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