The lifetime of an automatic transmission produced by the BW Company is normally distributed with a mean of 100,000 miles and a standard deviation of 20,000 miles.
a. What is the probability that the transmission will have a lifetime of at least 120,000 miles?
b. What is the probability that the transmission will have a lifetime of at least 60,000 miles?
c. What is the probability that the transmission will have a lifetime between 75,000 and 130,000 miles?
d. How many lifetime miles should BW guarantee if the company desires 97 percent of its transmissions to meet the guarantee?