No solution given.
", "variable_groups": [], "showQuestionGroupNames": false, "ungrouped_variables": ["p2", "p3", "b", "mm", "ch3", "ch1", "ch2", "p1", "t", "pd"], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "type": "question", "statement": "\nWhich of the following random variables could be modelled with a binomial distribution and which could be modelled with a Poisson distribution?
\nYou will lose 1 mark for every incorrect answer. The minimum mark is 0.
\n ", "preamble": {"js": "", "css": ""}, "tags": ["checked2015", "MAS1403", "MAS1604"], "parts": [{"choices": ["{ch1}", "{ch2}", "{ch3}"], "maxMarks": 0, "scripts": {}, "answers": ["Binomial Distribution", "Poisson Distribution"], "shuffleAnswers": false, "displayType": "radiogroup", "showCorrectAnswer": true, "minAnswers": 0, "shuffleChoices": true, "marks": 0, "maxAnswers": 0, "matrix": "mm", "layout": {"expression": "", "type": "all"}, "type": "m_n_x", "warningType": "none", "minMarks": 0}], "rulesets": {}, "variables": {"b": {"templateType": "anything", "description": "", "definition": "\n[\"20% of eggs from a family-run farm are bad. X is the number of bad eggs in a box of a dozen.\",\n \"A salesperson has a 50% chance of making a sale on a customer visit and she arranges 10 visits in a day. Let X be the number of sales that day.\",\n \"30% of items off a factory production line have been shown to have defects. Let A be the number of defectives in a box of 20 such items.\",\n \"One in ten new small businesses in the north-east goes bust within a year. Let X be the number of small businesses that fail in the next year out of thirty that have been set up.\",\n \"The probability that an office photocopier will fail on any given day is 0.15. The human resources office at Newcastle University has ten such photocopiers; Let Y be the number of photocopiers that fail today.\",\n \"Callers to the Vodaphone call centre will get through to an operator immediately with probability 0.25. X is the number of callers that speak to an operator immediately out of thirty such callers.\",\n \"Experience has shown that two in every ten components produced by a circuitboard company will be defective. A random sample of 100 components is inspected for defects, and D is the number of defectives in this sample.\"]\n", "group": "Ungrouped variables", "name": "b"}, "ch1": {"templateType": "anything", "description": "", "definition": "b[p1]", "group": "Ungrouped variables", "name": "ch1"}, "t": {"templateType": "anything", "description": "", "definition": "random(0,1)", "group": "Ungrouped variables", "name": "t"}, "p2": {"templateType": "anything", "description": "", "definition": "switch(t=0,random(0..abs(b)-1 except p1),random(0..abs(pd)-1 except p3))", "group": "Ungrouped variables", "name": "p2"}, "mm": {"templateType": "anything", "description": "", "definition": "[[1,-1],[1-2*t,2*t-1],[-1,1]]", "group": "Ungrouped variables", "name": "mm"}, "pd": {"templateType": "anything", "description": "", "definition": "\n[\"Y is the number of flights sold per hour by an online travel agency. This travel agency usually sells 10 flights per hour.\",\n \"X is the number of cars sold by a local garage in a month. This garage usually sells about 10 cars per month.\",\n \"The number of calls, Y, received at the British Passport Office in Durham occurs at the rate of 10 a minute.\",\n \"We are interested in X, the number of machine breakdowns in a day. Such breakdowns at a particular IT company occur at a rate of eight per week.\",\n \"X is the number of e-mails arriving in your inbox in a one hour period. On average you receive 3 e-mails per hour.\",\n \"On average, three patients arrive at a local Accident and Emergency department every hour. We count the number, X, of patients in an hour period.\",\n \"About five customers arrive at a fish shop queue every ten minutes during the lunch time rush. We count X, the number of customers arriving during the lunch time rush.\"]\n", "group": "Ungrouped variables", "name": "pd"}, "ch3": {"templateType": "anything", "description": "", "definition": "pd[p3]", "group": "Ungrouped variables", "name": "ch3"}, "p1": {"templateType": "anything", "description": "", "definition": "random(0..abs(b)-1)", "group": "Ungrouped variables", "name": "p1"}, "p3": {"templateType": "anything", "description": "", "definition": "random(0..abs(pd)-1)", "group": "Ungrouped variables", "name": "p3"}, "ch2": {"templateType": "anything", "description": "", "definition": "switch(t=0,b[p2],pd[p2])", "group": "Ungrouped variables", "name": "ch2"}}, "metadata": {"notes": "06/12/2013
\nReplaced a Poisson scenario that wasn't strictly Poisson. (AJY)
\n31/12/2012:
\n
Checked choices, OK. Added tag sc as examples can be easily added to via the arrays b and pd.
Given descriptions of 3 random variables, decide whether or not each is from a Poisson or Binomial distribution.
", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Are described variables from Poisson or binomial distributions?,", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}