The United States Marine Corps is reviewing its orders for uniforms because it has a surplus of uniforms for tall men recruits and a shortage for shorter men recruits. Its review involves data for 772 men recruits between the ages of 18 to 24. That sample group has a mean height of 69.7 inches with a population standard deviation of 2.8 inches. Construct a 99% confidence interval for the mean height of all men recruits between the ages 18 and 24.

And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.

Step-by-step explanation:

For this case we have the following sample size n =772 from men recruits between the ages of 18 to 24

represent the sample mean for the heigth

represent the population standard deviation

We want to construct a confidence interval for the true mean and we can use the following formula:

The confidence level is 0.99 or 99%o then the significance level is and and if we find for a critical value in the normal tandar ddistirbution who accumulates 0.005 of the area on each tail we got:

And replacing we got:

And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.

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