Question

in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.3 inches and a standard deviation of 2.0 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 65 inches. the probability that the study participant selected at random is less than 65 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 $x = 65$ (the value we are interested in), $\mu=69.3$ (the mean), and $\sigma = 2.0$ (the standard deviation). So, $z=\frac{65 - 69.3}{2.0}=\frac{- 4.3}{2.0}=-2.15$.

Step2: Find the probability using the standard normal distribution table

We want to find $P(X < 65)$, which is equivalent to $P(Z < - 2.15)$ when $X$ is normally distributed with mean $\mu$ and standard deviation $\sigma$ and $Z=\frac{X-\mu}{\sigma}$. Looking up the value of $P(Z < - 2.15)$ in the standard - normal distribution table, we get $0.0158$.

Answer:

$0.0158$