Question

A tire manufacturer would like to estimate the average tire life of its new all-season light truck tire in terms of how many miles it lasts. Determine the sample size needed to construct a 99% confidence interval with a margin of error equal to 2,400 miles. Assume the standard deviation for the tire life of this particular brand is 8,500 miles. The sample size needed is

Answer 1

The sample size needed to construct a 99% confidence interval with a margin of error equal to 2,400 miles is approximately 16,756.

Step-by-step explanation:

To determine the sample size needed to construct a 99% confidence interval with a margin of error equal to 2,400 miles, we can use the formula:

n = (Z-value)^2 * (standard deviation^2) / (margin of error)^2

Given that the standard deviation for the tire life is 8,500 miles and the margin of error is 2,400 miles, we can substitute these values into the formula:

n = (2.576)^2 * (8,500^2) / (2,400^2)

Simplifying the equation, we get:

n = 16,755.7766

Rounding up, the sample size needed is approximately 16,756. Therefore, the sample size needed is 16,756.