Question

this distribution of mens heights. the mean is 70 inches and the standard deviation is 2 inches. according to the empirical rule, 16% of mens heights are are below what value? a. 72 b. 74 c. 68 d. 66

Explanation:

Step1: Recall the Empirical Rule

The Empirical Rule (68 - 95 - 99.7 rule) for a normal - distribution states that approximately 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. The area below the mean is 50%. If 16% of the data is below a certain value, it means we are looking at a point that is 1 standard deviation below the mean.

Step2: Use the formula for the value in a normal - distribution

The formula for a value $x$ in a normal - distribution is $x=\mu+z\sigma$, where $\mu$ is the mean, $z$ is the z - score, and $\sigma$ is the standard deviation. For a point that is 1 standard deviation below the mean, $z=- 1$, $\mu = 70$ inches and $\sigma = 2$ inches.
Substitute the values into the formula: $x=\mu+z\sigma=70+( - 1)\times2$.
$x = 70 - 2=68$.

Answer:

c. 68