A corporation with several thousand employees wants to estimate the mean commute time for all employees. They would like to construct a 95% confidence interval with a margin of error of no more than 4 minutes. Preliminary interviews with a small sample suggest that a reasonable estimate of the population standard deviation is σ = 10 minutes. Which of the following is the smallest sample the company can take to achieve the desired margin or error?

A.5
B.24
C.25
D.41
E.42

C.25

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Which of the following is the smallest sample the company can take to achieve the desired margin or error?

This is n when

We have to round up.

So the correct answer is:

C.25

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step-by-step explanation: