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The top selling Red and Voss tire is rated 70,000 miles means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 miles and a standard deviation of 6,400.

a. What is the probability that a tire wears out before 70,000 miles.

b. What is the probability that a tire last more than 100,000 miles?

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    a) P(X<70000)=P((X-82000)/6400<(70000-82000¡­ Z-table=0.0303964

    b) P(X>100000)=P(Z>2.8125)=0.0024579

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