Question

The heights of women aged 20-29 follow approximately the N(63.8,2.8) distribution. Men the same age have heights distributed as N(69.7,3).

What percent of women aged 20-29 are taller than the mean height of men aged 20-29? (Enter your answer rounded to two decimal places.)

Answer 1

Solution:

For women, we are given

Mean = 63.8

SD = 2.8

For men, we are given

Mean = 69.7

We have to find P(X>69.7)

P(X>69.7) = 1 – P(X<69.7)

Z = (X – mean) / SD

Z = (69.7 - 63.8)/2.8

Z = 2.107143

P(Z<2.107143) = P(X<69.7) = 0.982447

(by using z-table)

P(X>69.7) = 1 – P(X<69.7)

P(X>69.7) = 1 – 0.982447

P(X>69.7) = 0.017553

Required percentage = 1.76%