Probability distributions Home Work

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Exercise 1 (10 points) Which of the following are continuous variables, and which are discrete? a. Number of traffic fatalities per year in the emirate of Ajman b. Distance a golf ball travels after being hit with a driver c. Time required to drive from home to AUS on any given day d. Number of ships in Port Khalid on any given day e. Your weight before breakfast each morning f. Speed of an airplane g. Age of a SBA professor chosen at random h. Number of books in the AUS bookstore i. The distance a car travels on a tank of gasoline j. The mark on a statistics quiz that consists of 10 multiple-choice questions Exercise 2 (15 points) The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. a. What is the probability that a patient would have to wait between one and two hours? b. What is the probability that a patient would have to wait exactly one hour? c. What is the probability that a patient would have to wait no more than one hour? Exercise 3 (15 points) Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, what is the probability that the response time will be a. between 5 and 10 minutes? b. less than 5 minutes? c. more than 10 minutes? 1 Exercise 4 (25 points) Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, there are limitations. Canadians visiting in the United States for more than 2 days are allowed to bring into Canada one bottle of liquor and one carton of cigarettes. A Canada customs agent has produced the following joint probability distribution of the number of bottles of liquor and the number of cartons of cigarettes imported by Canadians who have visited the United States for 2 or more days. Bottles of Liquor Cartons of Cigarettes 0 1 .63 .18 0 .09 .10 1 a. b. c. d. e. Find the marginal probability distribution of the number of bottles imported. Find the marginal probability distribution of the number of cigarette cartons imported. Compute the mean and variance of the number of bottles imported. Compute the mean and variance of the number of cigarette cartons imported. Compute the covariance and the coefficient of correlation. Exercise 5 (15 points) A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events? a. One out of the next four cars needs oil b. Two out of the next eight cars need oil c. Three out of the next 12 cars need oil Exercise 6 (10 points) Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week. a. Find the probability that the site gets 10 or more hits in a week. b. Determine the probability that the site gets 20 or more hits in 2 weeks. Exercise 7 (5 points) Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws? Exercise 8 (5 points) Find the following probabilities (a, b, c) and values of Z (d, e) a. P(−1.40 < Z < .60) b. P(Z> −1.44) c. P(Z < 2.03) d. Find z.045 e. Find z.20 2
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Probability distributions Home Work
Exercise 1 (10 points)
Which of the following are continuous variables, and which
are discrete?
a. Number of traffic fatalities per year in the emirate of
Ajman.
Discrete variable
b. ...


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