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 1600 miles. What warranty should the company use if they want 94% of the tires to outlast the warranty?

Answer 1

The warranty the company should use is of 57,520 mile.

Explanation:

Let X denote the tread life of a particular brand of tire.

It is provided that,
`X\sim N(60,000, 1600^(2))`.

Also provided that the company wants 94% of the tires to outlast the warranty.

Let x denote the warranty .

That is, P (X > x) = 0.94.

⇒ P (X < x) = 0.06

⇒ P (Z < z) = 0.06

The corresponding value of z is -1.55.

*Use a z-table.

Compute the value of x as follows:

`z=(X-\mu)/(\sigma)\\\\-1.55=(x-60000)/(1600)\\\\x=60000-(1.55* 1600)\\\\x=57520`

Thus, the warranty the company should use is of 57,520 mile.