Question

The average woman’s height is 65 inches with a standard deviation of 3.5 inches.What is the z-score for someone 72 inches tall? (round to the tenths place)What proportion of women are taller than 72 inches tall? % (enter answer as a percent rounded to the nearest hundredth as needed)

Answer 1

Mean= μ=65 inches

SD= σ =3.5 inches

(1) We want to firstly determine the z-score for someone 72 inches tall

-score of 72 = (x-μ )/σ

=(72-65)/3.5

= (7)/3.5

z-score of 72 = 2

(2) What proportion of women are taller than 72 inches tall?

The proportion of women that are taller than 72 inches tall = Probability of x>72

P(x>72) = 0.02275

In percentage, we have 0.02275 x 100 = 2.275%

To nearest hundredth, we have 2.28%

Hence, the proportion of women that are taller than 72 inches tall = 2.28% (nearest hundredth)