Continuing the previous exercise, use the normal approximation to the binomial to answer each of the questions posed in parts a through f. How well does the normal approximation perform in this case? Explain.
a. What is the probability that exactly five customers will buy life insurance from this agent in the coming month?
b. What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
c. What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
d. Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month.
e. What is the probability that the number of customers who buy life insurance from this agent in the coming month will lie within two standard deviations of the mean?
f. What is the probability that the number of customers who buy life insurance from this agent in the coming month will lie within three standard deviations of the mean?