4. Over the last 30 years, a company’s annual earnings increased year over year eighteen times and decreased year over year twelve times. You decide to model the number of earnings increases for the next decade as a binomial random variable. For Parts B, C, and D of this problem, assume the estimated probability is the actual probability for the next decade.
a. (2 points) What is your estimate of the probability of success, defined as an increase in annual earnings?
b. (3 points) What is the probability that earnings will increase in exactly 7 of the next 10 years?
c. (2 points) Calculate the expected number of yearly earnings increases during the next 10 years.
d. (3 points) Calculate the variance and standard deviation of the number of yearly earnings increases during the next 10 years.
