Business Data Analysis, A17, Test 2

Transcription

1 Business Data Analysis, A17, Test 2 Name: Student number 1. (2.5 marks) An executive is considering out of town business trip on Friday. She recognizes that at least one crises could occur at the company on the day she is gone. From previous experience she has constructed a probability distribution for the number of crises in a day at the company. Number of crises Probability a) Compute the expected value of the number of crises in a day. b) Compute the standard deviation.

2 2. (3 marks) Cathy and David own and operate a small bakery. They only bake and sell bread and pastries. Since the bakery is small it only accepts cash or Interac and 60% of their customers pay with cash. Of the customers who pay with cash 55% buy only bread, 15% buy only pastries and the rest buy both bread and pastries. Of the customers who pay with Interac 30% buy only bread, 25% buy only pastries and the rest buy both bread and pastries. a) Sketch a probability tree summarizing this information. b) What is the probability that a customer who bought both bread and pastries paid with Interac? c) What is the probability that a customer will buy pastries (only pastries or with bread)? 2

3 3. (3 marks) The contingency table below presents the results of a survey of 200 executives from 4 Canadian cities. The executives were asked to identify the geographic locale of their company and their company s industry type. The executives were only allowed to select one locale and one industry type. Toronto Calgary Vancouver Montreal Finance Manufacturing Communications Suppose that a respondent to this survey is selected at random. a) What is the probability that the respondent is from Montreal or from Toronto? b) What is the probability that the respondent is from Toronto or works in finance? c) What is the probability that the respondent is from Calgary if the respondent works in communications? d) What is the probability that the respondent works in communications if the respondent is from Calgary? e) Are industry type and location independent? Give a quantitative argument. 3

4 4. (3 marks) Arthur Andersen Enterprise group concluded a survey of US small business owners to determine the challenges for growth for their business. The top challenge, selected by 46% of small-business owners was the economy. A close second was finding qualified workers (37%). Suppose that 15% of the respondents selected both the economy and finding qualified workers as challenges for growth. A small business owner is selected at random. a) What is the probability that the owner believes that finding qualified workers is a challenge if the owner believes the economy is a challenge? b) What is the probability that the owner does not believe that the economy is a challenge if the owner believes finding qualified workers is a challenge? c) What is the probability that the owner believes that neither the economy is a challenge nor finding qualified workers is a challenge? 4

5 5. (2.5 marks) You own a company which employs 18 electricians. Parts of upstate New York have lost power due to a storm and you have volunteered to send some of your electricians to help. a) In how many ways can you select a group of 10 of your electricians to send to NY? b) In how many ways can you select 10 of your electricians to go to 10 different villages in NY? The license plates in NY have three letters followed by four numbers. c) How many NY license plates are possible? d) If one of your trucks got slightly dented by a car with NY license plates and the electrician who drove the truck only remembers that the plates of the offender start with KZ and end on either 5 or 6, how many NY license plates obey these constraints? 5

6 6. (2 marks) A bank branch has an average arrival rate of 3.2 customers every 4 minutes. a) What is the probability that no customers will arrive in two minutes? b) What is the probability that precisely 25 customers will arrive in half an hour? 7. (2 marks) You are a home insurance claims adjuster and currently you have 48 open claims of which 29 are in the city and 19 are in the suburbs. You will visit six of the houses today, selected at random. a) What is the probability that four of the houses selected for a visit are in the city? b) What is the probability that less than three of the houses you will visit today are in the suburbs? c) What is the expected value and the standard deviation for the number of houses in the suburbs you will visit today? 6

7 8. (2 marks) According to the Financial Planners Standards Council, 31% of certified financial planners (CFP s) earn $150,000 or more per year. Suppose that a random sample of 15 CFP s is selected. a) What is the probability that more than three CFP s in this sample earn more than $150,000 per year? b) What is the expected number of CFP s in this sample who earn more than $150,000 per year and what is the standard deviation? Various Formulas p(a B) = p(a) + p(b) p(a B) p(a B) = p(a)p(b A) p(a B) = p(b A)p(A) p(b) np k = n! (n k)!, nc k = n! (n k)!k! E(X) = xp(x), V ar(x) = x 2 p(x) E(X) 2, σ = V ar(x) p(x) = n C x p x (1 p) n x, E(X) = np, V ar(x) = np(1 p) p(x) = k C x N k C n x NC n, E(X) = np, V ar(x) = np(1 p) N n N 1, p = k N. p(x) = e λ λ x, E(X) = λ, V ar(x) = λ. x! 7