In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions about X, the number of customers who will buy life insurance from this agent in the coming month:
a. What is the probability X is exactly 5?
b. What is the probability that X is no more than 10?
c. What is the probability that X is at least 20?
d. Determine the mean and standard deviation of X.
e. What is the probability that X will be within two standard deviations of the mean?
f. What is the probability that X will be within three standard deviations of the mean?