Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had been involved in traffic accidents at the rate of 1,000 per year. Suppose the number of crashes involving vehicles on operational duties follows a Poisson distribution. a. What is the average number of days between successive crashes? b. What is the rate parameter of the appropriate exponential distribution? c. What is the probability that the next vehicle will crash within a day?
A committee of 10 is to be chosen from 50 people, 25 of whom are Republicans and 25 Democrats. The committee is chosen at random. a. What is the probability that there will be five Republicans and five Democrats? b. What is the probability that a majority of the committee will be Republicans?
Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none. a. What is the probability that a customer buys three tires? b. Construct a cumulative probability distribution for the number of tires bought.
Comcast Corporation is a global telecommunications company headquartered in Philadelphia, PA. Generally known for reliable service, the company periodically experiences unexpected service interruptions. When service interruptions do occur, Comcast customers who call the office receive a message providing an estimate of when service will be restored. Suppose that for a particular outage, Com cast customers are told that service will be restored in two hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution. a. What is the probability that the cable service will be repaired in one hour or less? b. What is the probability that the repair will take between one hour and two hours? c. For a customer who calls the Comcast office at 1:00 p.m., what is the probability that the cable service will not be repaired by 5:00 p.m.?
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