Question

In a certain​ city, the average​ 20- to​ 29-year old man is 72.5 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.5 inches​ tall, with a standard deviation of 3.8 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

Answer 1

Answer:

​ 70-inch woman is taller.

Step-by-step explanation:

Given data:

For men

age group = 20 - 29 year

Height = 72.5 inches

standard deviation = 3.2 inches

For women

age group = 20 - 29 year

Height = 64.5 inches

standard deviation = 3.8 inches

To find:

who is taller?  a​ 75-inch man or a​ 70-inch woman?

To find that, firstly we find z- score for each gender.

Solve:

Z-score=(x-μ)/σ

where:

μ=mean

σ=std deviation

Z(men) = (75-72.5)/3.2

            = 0.781

Z(women) = (70-64.5)/3.8

               = 1.447

From the above, the z-score for the woman is relatively larger than that of the man, this means that the woman is taller.