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 (round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 68$ (the value we are interested in), $\mu=69.7$ (the mean), and $\sigma = 4.0$ (the standard deviation).
$z=\frac{68 - 69.7}{4.0}=\frac{- 1.7}{4.0}=-0.425$

Step2: Find the probability

We use the standard normal distribution table (or z - table) to find the probability corresponding to $z=-0.425$. Looking up the value in the z - table, the probability $P(Z < - 0.425)$ is approximately $0.3352$.

Answer:

$0.3352$