The sticker price for a new luxury SUV is \(\$ 93,755\), and most people who are interested in purchasing the vehicle will try to negotiate the price. To help in the negotiation process, there are many websites that provide information about what other consumers have paid for the vehicle. What is very interesting is that the price paid tends to follow the pattern of a normal distribution. If the average price paid for this vehicle is \(\$ 92,450\) and if the standard deviation is \(\$ 1,275\), find each of the following:

a. What is the probability that a buyer will pay more than the average price?

b. What is the probability that a buyer will pay less than \(\$ 92,000\) ?

c. What is the probability that a buyer will pay between \(\$ 91,500\) and \(\$ 93,000\) ?

d. At what price will \(95 \%\) of the buyers pay more?

e. What is the range of prices paid for the middle \(95 \%\) of the buyers?