FDIC bank failures. The Federal Deposit Insurance Corporation (FDIC) normally 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 20 years, the average number of bank failures per year among insured banks was 29 (FDIC Failed Bank List, 2019). Assume that x, the number of bank failures per year among insured banks, can be adequately characterized by a Poisson probability distribution with mean 29.

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

b. In 2010, 157 banks failed. How far (in standard deviations) does x = 157 lie above the mean of the Poisson distribution? That is, find the z-score for x = 157.

c. In 2019, 4 banks failed. Find P1x … 42.