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?

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

Step-by-step explanation:

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

It is provided that,  .

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:

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

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