Question

A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 40,000 miles and a standard deviation of 4,000 miles. The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased qualify the guarantee mileage. What should the guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage? (2 points)

Answer 1

Answer:

The guaranteed mileage should be 31800 miles.

Step-by-step explanation:

Consider the provided information.

It is given that the normally distributed with a mean of 40,000 miles and a standard deviation of 4,000 miles. Also the company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage.

That means the p < 0.02

Now with the help of the table the respective Z-score value of p < 0.02 is  -2.05

From the provided information mean and standard deviation is given as $\mu = 40,000\ \text{and}\ \sigma = 4000$

Now use the formula: $z=\frac{x-\mu}{\sigma}$

Substitute the respective values in the above formula.

$-2.05=\frac{x-40000}{4000}$

$-8200=x-40000$

$-8200+40000=x$

$31800=x$

Hence, the guaranteed mileage should be 31800 miles.