Some of the variables that affect the monthly payment of a new-car loan are the total amount borrowed, the interest rate, and the length of the loan. During the fourth quarter of 2012, the mean length...

Some of the variables that affect the monthly payment of a new-car loan are the total amount borrowed, the interest rate, and the length of the loan. During the fourth quarter of 2012, the mean length of a new-car loan was 65 months, a record high according to Experian.28 Suppose the length of a new-car loan is approximately normal with standard deviation nine months.

a. What is the probability that a new-car loan is for at most 48 months?

 b. What is the probability that a new-car loan length is between 50 and 70 months?

 c. Find a symmetrical interval about the mean such that 95% of all new-car loan lengths fall in this interval.

d. Suppose the amount borrowed on a new-car loan is also approximately normal with mean $20,000 and standard deviation $5000. If the length of the loan and the amount borrowed are independent, what is the probability that the loan will be for more than $27,000 and for less than 60 months?