Approximately 80% of American families have some form of life insurance coverage. For a randomly selected sample of n = 15 families, and the discrete random variable x = the number of families in the sample who are covered by life insurance:
a. Calculate the mean and the standard deviation of the binomial distribution.
b. Using the binomial distribution, calculate the probability that x will be exactly 12 families.
c. Repeat part (b), using the normal approximation to the binomial.
d. Using the normal approximation to the binomial, find the probability that at least 10 families in the sample will be covered by some form of life insurance.