Question

The distribution of heights of adult American men is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions:

(d) A height of 71.5 inches corresponds to what percentile of adult male American heights?

==> I already know the answer is the 84th percentile, but how do you get this answer?

Answer 1

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.

Answer 2

So since its asking you to use the empirical rule. if you notice 71.5 is 2.5 inches higher than 69. So 71.5 is exactly 1 standard deviation above the mean which we know is 68%. 50% + (68/2) = 84%