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?

70-inch woman is taller.

Step-by-step explanation:

Given dа ta:

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.