Question

The heights of 18 year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches. What is the probability that an 18 year-old man selected at random is between 68 and 70 inches tall?

Answer 1

0.6826

Explanation:

It is given that the heights of 18 year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches.

Let X be the heights of 18 year-old men

X is N(69, 2)

the probability that an 18 year-old man selected at random is between 68 and 70 inches tall

=
`P(68<x<70)`

we convert x score into Z score and then use table to find out the probability

We have
`z=(x-69)/(2)`

Thus the probability that an 18 year-old man selected at random is between 68 and 70 inches tall

=
`P(68<x<70)`

=
`P(-1<x<1)\\=0.6826`