Question

The heights of English men are normally distributed with a mean of 71.5 inches and a standard deviation of 2.5 inches. According to the Expanded Empirical Rule, what percentage of English men are: (a) Between 69 and 74 inches tall?

Answer:

(b) Over 73.175 inches tall?

Answer:

(c) Under 66.5 inches tall?

Answer:

Answer 1

(a) Between 69 and 74 inches tall?

Easiest way to find probability of men between 69 and 74 inches tall is to find probability < 74and subtract the probability < 69

Easiest way to find probability of 69 and 74 is to calculate z score of each

z score of 69 = (x-mean)/std = (69-71.5)/2.5 = -1 using a z table gives us prob < 69 is .1587

z score of 74 = (x-mean)/std = (74-71.5)/2.5 = 1 using a z table gives us prob < 74 is .8413

Subtract the .1587 from .8413 gives us .6826 or 68.26 %

(b) Over 73.175 inches tall?

mean +/- 1 SD
71.5 +/- 2.5 = (69,74)

32% fall between 69 and 74
16% fall outside of this interval

(c) Under 66.5 inches tall?

mean +/- 2 SD

71.5 +/- 2(2.5) = (66.5,76.5)

5% fall above 76.5 and 66.5

Therefore, 2.5% are under than 66.5