To determine whether they need to hire extra help for the holiday season, the managers of a railroad company want to estimate ho

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8 days ago

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To determine whether they need to hire extra help for the holiday season, the managers of a railroad company want to estimate ho

w long, on average, it takes a crew to unload a freight car at the Lafayette station. They will calculate an estimator as the sample mean of a random sample of unloading times. The managers want the sample mean to have a standard error of 1.51.5 minutes. The corporate office has provided a standard deviation of 99 minutes to use for calculation purposes. How large should the random sample be to ensure the sample mean has the desired standard error?

Mathematics

1 answer:

Svet_ta [9.5K] · Answer 1 · 2026-03-19T21:05:06+03:00

The answer is 36. Given data includes a standard error of 1.5 minutes and a standard deviation of 9 minutes. When working with sample size n, the standard error can be expressed as (standard deviation) ÷ √n. This means that 1.5 = 9 ÷ √n. Thus, √n equals 9 ÷ 1.5, which yields √n = 6. Consequently, squaring both sides provides n = 6², resulting in 36.