Your job as the assistant to the police chief in DC requires that you advise the police chief on departmental policy. The Washington Post recently published an article (11/15/98) claiming that the DC police department has a higher rate of fatal shootings per 1,000 officers than other departments. In doing your reading, you find that the distribution of shootings per 1,000 police officers in cities of is normally distributed with a mean of 1.6 and a standard deviation of .20.

a. What is the Z score for a police department with 1.9 deaths per 1,000 officers?

b. What is the probability that a department would have a fatal shooting rate per 1,000 officers of 1.5 or less?

c. Suppose that DC had a rate of 2.3 shootings per 1,000 police officers last year, and the chief asks you if you think that DC has an unusually high fatal shooting rate. What do you tell him? Explain.

d. Suppose the Chief decides he needs to lower the fatal shooting rate, and he sets as a goal for the first year being in the 75th percentile, meaning that at least 25% of all other cities have to have a higher fatal shooting rate than DC. What is the cutoff value?