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# The tread life of a particular brand of tire is a random ...

### Resolved Question:

The tread life of a particular brand of tire is a random variable best descrided by a normal distribution with a mean of 60,000 miles and standard deviation of 12,000 miles. What is the probability a particular tire of this brand will last between 62,160 and 62,520 miles?
Submitted: 10 years ago.
Category: Homework
Expert:  mathsmart replied 10 years ago.
Hello,

You need to find the Z-scores corresponding to 62,160 and 62,520

Z = (x - μ)/σ

So the Z-score for 62,160 is:

(62,160 - 60,000)/12,000 = .18

The Z-score for 62,520 is:

(62,520 - 60,000)/12,000 = .21

Using a calculator the area under the curve corresponding to the interval of .18 to .21 is approximately .0117, so the probability is approximately 1.17%.

Customer: replied 10 years ago.
is this only part a?
Expert:  mathsmart replied 10 years ago.
Hello,

There was only one question in your problem. Is there something you forgot to type in?
Customer: replied 10 years ago.
no, there was an a,b and c

b.If the manufacturer gaurantees the tread life of this brand will last between 58,620 miles, what proportion of the tires will need to be replaced under warranty?

c. If the manufacturer sells 500,000 of these tire, how many would you expect to need replaced under warranty?
Expert:  mathsmart replied 10 years ago.