Question

use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 71 miles per hour, with a standard deviation of 5 miles per hour. estimate the percent of vehicles whose speeds are between 66 miles per hour and 76 miles per hour. (assume the data set has a bell - shaped distribution.)
approximately (square%) of vehicles travel between 66 miles per hour and 76 miles per hour

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 data - point. For $x = 66$, $z_1=\frac{66 - 71}{5}=\frac{-5}{5}=-1$. For $x = 76$, $z_2=\frac{76 - 71}{5}=\frac{5}{5}=1$.

Step2: Apply the Empirical Rule

The Empirical Rule for a normal (bell - shaped) distribution states that approximately 68% of the data lies within 1 standard deviation of the mean, that is, between $z=-1$ and $z = 1$.

Answer:

68