Economics and Finance
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?