Question

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2800 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty?

Answer 1

Answer:

z=(x-mean)/sd

>=(57700-60000)/2300

>= -1

That is 0.8413.

Answer 2

55,100

Given:

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2800 miles

To find:

What warranty should the company use if they want 96% of the tires to outlast the warranty

Solution:

We can determine the tread life by, simply insert a penny with Lincoln's head upside down and facing you into the tread groove of your tire. If you can see all of Lincoln's head, your tread depth is less than 2/32 inch and your tires need to be replaced.

Want the 4th percentile z of a normal distribution, and 96% will be above that number

⇒ z= $\frac{(x-60000)}{2800}$ = -1.75

⇒ x-60000=-4900

⇒ x=55,100

Hence, the company should use 55,100 warranty.

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