Question

in the united states, the mean average height of adult men is approximately 70 inches, with a standard deviation of 3 inches. if height is normally distributed, which of the following percentages represents the number of men in this country who are between 67 and 73 inches tall? 68% 95% 34% 16%

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 67$, $z_1=\frac{67 - 70}{3}=\frac{- 3}{3}=-1$. For $x = 73$, $z_2=\frac{73 - 70}{3}=\frac{3}{3}=1$.

Step2: Use the empirical rule

The empirical rule for a normal distribution states that approximately 68% of the data lies within 1 standard deviation of the mean. That is, the percentage of data between $z=-1$ and $z = 1$ is 68%.

Answer:

68%