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 98% confidence interval with a margin of error equal to 3 comma 000 miles. Assume the standard deviation for the tire life of this particular brand is 9 comma 000 miles. The sample size needed is nothing. (Round up to the nearest integer.)

Sample size of at least 49 must be needed .

Step-by-step explanation:

We are given that a 98% confidence interval is constructed with a margin of error equal to 3,000 miles. Assume the standard deviation for the tire life of this particular brand is 9,000 miles.

So, Margin of error formula is given by =

where, = significance level which is 2%

            = standard deviation = 9,000 miles

            n = sample size

Here, the value of z score at 2% significance level is 2.3263 .

So, margin of error = 2.3263 *

                        =

                              = 6.9789

                         n = = 48.7 or ≈ 49 (approx)

Therefore, sample size of at least 49 must be needed .

answer: 40.95

step-by-step explanation: