Question

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

Answer 1

Answer:

36

Step-by-step explanation:

Data provided in the question:

Standard error = 1.5 minutes             ( ∵ number are repetitive 1.51.5 )  

Standard deviation = 9 minutes        ( ∵ number are repetitive 99 )

Now,

Standard error = ( Standard deviation ) ÷ √n

Here,

n is the sample size

Therefore,

on substituting the respective values, we get

1.5 = 9 ÷ √n

or

√n = 9 ÷ 1.5

or

√n = 6

or

n = 6² = 36