We intend to estimate the average break time of Dunder Mifflin employees. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 6 minutes. We want our 99 percent confidence interval to have a margin of error of no more than plus or minus 2 minutes. What is the smallest sample size that we should consider?

The minimum sample size that we should consider is of 60 employees.

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.

We want our 99 percent confidence interval to have a margin of error of no more than plus or minus 2 minutes. What is the smallest sample size that we should consider?

We need to find n for which

So

Simplifying by 2

Rounding up

The minimum sample size that we should consider is of 60 employees.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.