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 2900 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty?

Answer 1

it is given that the population mean and population standard deviation

We want to find the warranty limit so that 96% of the tires outlast the warranty

Using z distribution for significance level = 1-0.96 = 0.04

We will consider the left tailed distribution to find z critical value. For 0.04 significance level in z distribution table

we get z critical = -1.75

Now, using the formula

setting the given values, we get

-1.75 = (x - 60000)/2900

by cross multiplication, we get

-1.75*2900 = x-60000

-5075 = x - 60000

adding 60000 on each side, we get

-5075 + 60000 = x - 60000 + 60000

This gives us

x = 54925 miles

Therefore, required answer is 54925 miles