Solution Found!
FDIC bank failures. The Federal Deposit Insurance
Chapter 4, Problem 70E(choose chapter or problem)
Problem 70E
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 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 distribution 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 distribution? That is, find the z-score for x = 360.
c. In 2010, 65 banks failed. Find P(x ≤ 65)
Questions & Answers
QUESTION:
Problem 70E
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 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 distribution 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 distribution? That is, find the z-score for x = 360.
c. In 2010, 65 banks failed. Find P(x ≤ 65)
ANSWER:
Solution 70E
Step1 of 4:
Let us consider a random variable X it presents the number of bank failures per year among insured banks. And X follows poisson distribution with parameter
Here our goal is:
a). We need to find the expected value and standard deviation of x.
b). We need to check whether x = 360 lie above the mean of the Poisson distribution.
c). We need to find
Step2 of 4:
a).
Let,
We know that mean of poisson distribution is