Question

a) Assume that the height (in inches) of an American female is normal with expected value 64 inches and standard deviation 2.5. Also, assume that the height of an American male is normal with expected value 69 inches and standard deviation of 3.0 inches. A man and a woman are chosen at random. The woman’s height is measured, and she is found to be exactly 68.2 inches tall. How much taller do we expect the man to be (as compared to this particular woman)?

Answer 1

First we will find out the probability of that an american female have height greater than 68.2 and then used the probability to compare with their male counter part

This is a normal distribution question with


P(x > 68.2)=?
The z-score at x = 68.2 is,

This implies that

PS: you have to refer z score table to find the final probabilities.

We will reverse
now, we will find the value of x from the probability (hence, z score) calculated in above part to get the exact height of an american male

This is a normal distribution question with


p = 0.0465
Given in the question
P(X > x) = 0.0465
This implies that
P(Z > 1.6797806567981286) = 0.0465
With the help of formula for z, we can say that


PS: you have to refer z score table to find the final probabilities.