# Question: A local law enforcement agency claims that the number of

A local law enforcement agency claims that the number of times that a patrol car passes through a particular neighborhood follows a Poisson process with a mean of three times per nightly shift. Let x denote the number of times that a patrol car passes through the neighborhood during a nightly shift.

a. Calculate the probability that no patrol cars pass through the neighborhood during a nightly shift.

b. Suppose that during a randomly selected night shift no patrol cars pass through the neighbor-hood. Based on your answer in part a, do you believe the agency’s claim? Explain.

c. Assuming that nightly shifts are independent and assuming that the agency’s claim is correct, find the probability that exactly one patrol car will pass through the neighborhood on each of four consecutive nights.

a. Calculate the probability that no patrol cars pass through the neighborhood during a nightly shift.

b. Suppose that during a randomly selected night shift no patrol cars pass through the neighbor-hood. Based on your answer in part a, do you believe the agency’s claim? Explain.

c. Assuming that nightly shifts are independent and assuming that the agency’s claim is correct, find the probability that exactly one patrol car will pass through the neighborhood on each of four consecutive nights.

**View Solution:**## Answer to relevant Questions

When the number of trials, n, is large, binomial probability tables may not be available. Furthermore, if a computer is not available, hand calculations will be tedious. As an alternative, the Poisson distribution can be ...Suppose that you purchase (randomly select) 3 TV sets from a production run of 10 TV sets. Of the 10 TV sets, 9 are destined to last at least five years without needing a single repair. What is the probability that all three ...A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on ...Describe how to compute the standard deviation of a discrete random variable, and interpret what this quantity tells us about the observed values of the random variable. Explain what the mean, μ, tells us about a normal curve, and explain what the standard deviation, σ, tells us about a normal curve.Post your question