The Federal Deposit Insurance Corporation (FDIC), insures deposits of up to $100,000 in banks that are members of the Federal Reserve System against losses due to bank failure or theft. Over the last 5 years, the average number of bank failures per year among insured banks was 4.4

(FDIC, Nov. 1999). Assume that x, the number of bank failures per year among mured banks, can be adequately characterized by a Poisson probability distribution with mean 4.

a. Find the expected value and standard deviation of x.

b. In 1997, only one insured bank failed. How far (in standard deviations) does x = 1 lie below the mean of the Poisson distribution? That is, find the z-score for x = 1.

c. In 1999, six insured banks failed. Find P(x 5 6).

d. Discuss conditions that would make the Poisson assumption plausible.