The Federal Deposit Insurance Corporation (FDIC) normally insures deposits of up to $100,000 in banks that are

Question:

The Federal Deposit Insurance (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 10 years, the average number of bank failures per year among insured banks was 45 (FDIC Failed Bank List, Dec. 2011). Assume that x, the number of bank failures per year among insured banks, can be adequately characterized by a Poisson probability with mean 45.
a. Find the expected value and standard deviation of x.
b. In 2011, 360 banks failed. How far (in standard deviations) does x = 360 lie above the mean of the Poisson That is, find the z-score for x = 360.
c. In 2010, 65 banks failed. Find P(x ≤ 65) Corporation
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