Question

use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 62 miles per hour and 78 miles per hour. (assume the data set has a bell - shaped distribution.)
approximately % of vehicles travel between 62 miles per hour and 78 miles per hour

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard - deviations 62 and 78 are from the mean. For 62: $\frac{70 - 62}{4}=\frac{8}{4}=2$ standard - deviations below the mean. For 78: $\frac{78 - 70}{4}=\frac{8}{4}=2$ standard - deviations above the mean.

Step2: Apply the Empirical Rule

The Empirical Rule states that for a bell - shaped distribution, approximately 95% of the data lies within 2 standard - deviations of the mean.

Answer:

95