Total loss A total-loss insurance policy pays $15,000 against a premium of $500 if a car is considered a total loss. A company estimates that for such policies, the probability a car is considered a total loss is 0.0015. In a portfolio of n policies of this type, let X be the number of total loss cases.

a. Find the mean of the distribution of X in terms of n.

b. How large an n is needed so that ten total loss cases are expected to occur?

c. Using the value of n found in part

b, find the expected return of this company’s portfolio.