Question

use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 69 miles per hour, with a standard deviation of 5 miles per hour. estimate the percent of vehicles whose speeds are between 64 miles per hour and 74 miles per hour. (assume the data - set has a bell - shaped distribution.)
approximately % of vehicles travel between 64 miles per hour and 74 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 $x = 64$, $\mu=69$, and $\sigma = 5$, $z_1=\frac{64 - 69}{5}=\frac{-5}{5}=-1$. For $x = 74$, $\mu = 69$, and $\sigma=5$, $z_2=\frac{74 - 69}{5}=\frac{5}{5}=1$.

Step2: Apply the Empirical Rule

The Empirical Rule (68 - 95 - 99.7 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