Question

in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.7 inches and a standard deviation of 4.0 inches. a study participant is randomly selected. complete parts (a) through (d) below.
(a) find the probability that a study participant has a height that is less than 68 inches.
the probability that the study participant selected at random is less than 68 inches tall is 0.3352 (round to four decimal places as needed.)
(b) find the probability that a study participant has a height that is between 68 and 72 inches.
the probability that the study participant selected at random is between 68 and 72 inches tall is (round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 69.7$ (mean), $\sigma = 4.0$ (standard deviation).
For $x = 68$, $z_1=\frac{68 - 69.7}{4.0}=\frac{-1.7}{4.0}=- 0.425$.
For $x = 72$, $z_2=\frac{72 - 69.7}{4.0}=\frac{2.3}{4.0}=0.575$.

Step2: Use the standard normal distribution table

We know that $P(68$P(-0.425From the standard - normal table, $P(Z < 0.575)\approx0.7177$ and $P(Z < - 0.425)\approx0.3352$.
So $P(-0.425

Answer:

$0.3825$