// Numbas version: exam_results_page_options
{"name": "Probability", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Probability", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A coffee shop chain would like to reduce costs by introducing a new cheaper blend of coffee, but before they make the change, they decide to test how many customers will notice the difference. They test the new blend in two locations; Birmingham and Southampton. 2000 customers took part in the survey. 800 from Birmingham and 1200 from Southampton.</p>\n<p>96 of the customers in Birmingham answered &lsquo;Yes I can taste the difference&rsquo;.</p>\n<p>240 of the customers in Southampton answered &lsquo;Yes I can taste the difference&rsquo;.</p>", "advice": "<p>Provide your answers to 3 decimal places.</p>", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Determine the probability that a customer will not taste the difference. Give your answer to (3 decimal places).</p>", "minValue": "0.831", "maxValue": "0.833", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Given that a customer answers &lsquo;yes I can taste the difference&rsquo; what is the probability that they are from Birmingham?&nbsp;Give your answer to (3 decimal places).</p>", "minValue": "0.285", "maxValue": "0.287", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The coffee shop believes that only 5% of customer will switch to a competitor if they introduce the cheaper coffee blend. The coffee shop chain take a sample of 50 customers.</p>\n<p>Calculate the probability that exactly 4 customers in this sample state that they will switch to a competitor.&nbsp;Give your answer to (3 decimal places).</p>", "minValue": "0.135", "maxValue": "0.137", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>State which probability distribution you used in part c).</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Normal Distribution", "Binomial Distribution", "Poisson Distribution"], "matrix": [0, "2", 0], "distractors": ["", "", ""]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>State two assumptions of that distribution.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "choices": ["Two potential outcomes for each trial", "Probability of success for each outcome is same", "Number of trial is not fixed", "Probability of success and failure for each outcomes are equaly likely"], "matrix": ["1", "1", 0, 0], "distractors": ["", "", "", ""]}], "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}]}]}], "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}]}