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# Useful Life of a Radial Tire

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The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The company makes 10,000 tires a month.

a. About how many tires will last between 25,000 and 35,000 miles?

b. About how many tires will last more that 40,000 miles?

c. About how many tires will last less than 25,000 miles?

d. what is the probability that if you buy a radial tire at random, it will last between 20,000 and 35,000 miles?

#### Solution Preview

The useful lfe of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The company makes 10,000 tires a month.

a. About how many tires will last between 25,000 and 35,000 miles?

We need to know the probability that a radial tire will last between 25,000 and 35,000 miles. It equals

P(25000<X<35000)=0.6827
So,

...

#### Solution Summary

This solution calculates the probability of a useful life of a radial tire in varying distances. All steps and formulas are shown with brief explanations.

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