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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...

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?

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