Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 95% confident that the sample mean is within 5 minutes of the true population mean

The minimum sample size is needed to be 95% confident that the sample mean is within 5 minutes of the true population mean is 40.

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.

If the population standard deviation is 16 minutes, what minimum sample size is needed to be 95% confident that the sample mean is within 5 minutes of the true population mean

This is n when . So

The minimum sample size is needed to be 95% confident that the sample mean is within 5 minutes of the true population mean is 40.