use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 69 miles per…
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.)\napproximately % of vehicles travel between 64 miles per hour and 74 miles per hour.
Answer
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