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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

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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 7,500 miles.

The sample size needed is ___.

?(Round up to the nearest? integer.)