# The heights of males in a certain country are normally distributed with a mean of 70.2 inches and a standard deviation of 4.2 inches. What is the probability that a randomly chosen male is under the height of 65 inches?

##### 1 Answer

Since 65 is (approx.) -1.24 standard deviations from the mean of 70.2,

#### Explanation:

If

#P(X < x)= P(Z< (x-mu)/sigma).#

This means we can find the probability

Let

#P(X < 65)=P(Z < (65-70.2)/4.2)#

#color(white)(P(X < 65)) ~~ P(Z < "–"1.24)#

What this means is that the point in the

Why bother "transforming" *any* normal random variable to this base one.

The table we so happen to make is for

From the table,

#P(X < 65) ~~ 0.1075# .