MSBA 6120 Summer, 2014 Name __________________

Practice Exam 1 This is to be worked on your own and turned in Tuesday, July 8, by 4:30 PM in 3-150

(You can leave it with the receptionist or place it in Anna Errores mailbox) A key will be made available on Wednesday morning, July 9

Problem 1. a) A developer of a new subdivision offers a prospective home buyer a choice of four designs, three different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer? b) The same developer wishes to build 9 houses, each a different design. In how many ways can he place these houses on a street if six lots are on one side of the street and three lots are on the opposite side?

Problem 2. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that: a) At least one member of a married couple will vote? b) A wife will vote, given that her husband will vote? c) A husband will vote, give that his wife will not vote?

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Problem 3. A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 5% of the rooms at the Ramada Inn, in 4% of the rooms at the Sheraton, and in 8% of the rooms at the Lakeview Motor Lodge, what is the probability that: a) a client will be assigned a room with faulty plumbing b) a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? Problem 4. Let X be the random variable that represents the number of heads minus the number of tails obtained in three tosses of a balanced coin. a) List the elements of the sample space for the three tosses of a coin and assign the value of X to each element. b) Give the probability distribution of the random variable X.

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Problem 5. In an NBA (National Basketball Association) championship series, the team that wins four games out of seven is the winner. Suppose that teams A and B face each other in the championship games and that team A has probability 0.55 of winning a game over B. a) What is the probability that team A will win the series in 6 games? b) What is the probability that team A will win the series? Problem 6. An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience catastrophe is a Poisson random variable with = 0.5. a) What is the probability that at most 3 cars per year will experience a catastrophe? b) What is the probability that more than one car per year will experience a catastrophe?

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Problem 7. A continuous random variable X that can assume values between x = 0 and x = 1 has a density function given by f (x) = cx4 , where c is a positive constant. Find: a) The value of c that will make f(x) density function. b) FX (x) . c) P(X < 0.5). d) Find F1(p) and use it to find the median of the distribution of X.