// Numbas version: exam_results_page_options
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z_{\\alpha/2}) = 0.975$.</p>\n<p>We know that:</p>\n<p>$z_{{\\alpha}/2} =&nbsp;z_{0.025} = 1.96$ (from the table of Normal distribution),</p>\n<p>Therefore, the 95% confidence interval for &micro; will be:</p>\n<p>\\[ \\big[ \\var{xbar} - 1.96 \\times&nbsp;\\frac{\\var{sigma}}{\\sqrt{\\var{n}}} ,\\var{xbar} +&nbsp;1.96 \\times&nbsp;\\frac{\\var{sigma}}{\\sqrt{\\var{n}}} \\big] \\]</p>\n<p>\\[ [ \\var{ci_lower}&nbsp;, \\var{ci_upper}&nbsp;] \\]</p>\n<p></p>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(10..200)", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Ungrouped variables", "definition": "random(0.99*mu..1.01*mu)", "description": "", "templateType": "anything", "can_override": false}, "sigma": {"name": "sigma", "group": "Ungrouped variables", "definition": "random(0.5..10 #0.1)", "description": "", "templateType": "anything", "can_override": false}, "ci_percent": {"name": "ci_percent", "group": "Ungrouped variables", "definition": "95", "description": "", "templateType": "anything", "can_override": false}, "alp": {"name": "alp", "group": "Ungrouped variables", "definition": "((100-ci_percent)/2)/100", "description": "", "templateType": "anything", "can_override": false}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "random(2..100 #0.1)", "description": "", "templateType": "anything", "can_override": false}, "ci_lower": {"name": "ci_lower", "group": "Ungrouped variables", "definition": "precround(xbar - 1.96*sigma/sqrt(n),2)", "description": "", "templateType": "anything", "can_override": false}, "ci_upper": {"name": "ci_upper", "group": "Ungrouped variables", "definition": "precround(xbar + 1.96*sigma/sqrt(n),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "xbar", "sigma", "ci_percent", "alp", "mu", "ci_lower", "ci_upper"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>[[[0]],&nbsp;[[1]]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(ci_lower,2)", "maxValue": "precround(ci_lower,2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(ci_upper,2)", "maxValue": "precround(ci_upper,2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ed Southwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2415/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ed Southwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2415/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}