4.87 A car salesperson estimates the following probabilities for the number of cars that she will sell in the next week:

Number of cars 0 1 2 3 4 5 Probability 0.10 0.20 0.35 0.16 0.12 0.07

a. Find the expected number of cars that will be sold in the week.

b. Find the standard deviation of the number of cars that will be sold in the week.

c. The salesperson receives a salary of $250 for the week, plus an additional $300 for each car sold.

Find the mean and standard deviation of her total salary for the week.

d. What is the probability that the salesperson’s salary for the week will be more than $1,000?