The U. S. Department of Health and Human Services collected sample data for 772 males between the ages of 18 and 24. That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches. Find the 99 percent confidence interval for the mean height of all males between the ages of 18 and 24.

The 99 percent confidence interval for the mean height of all males between the ages of 18 and 24 is between 69.44 inches and 69.96 inches.

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 M as such

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

The lower end of the interval is the mean subtracted by M. So it is 69.7 - 0.26 = 69.44 inches

The upper end of the interval is the mean added to M. So it is 69.7 + 0.26 = 69.96 inches.

The 99 percent confidence interval for the mean height of all males between the ages of 18 and 24 is between 69.44 inches and 69.96 inches.