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 4 miles per hour. Estimate the percent of vehicles whose speeds are between 63 miles per hour and 79 miles per hour.​ (Assume the data set has a​ bell-shaped distribution.) Approximately what ​% of vehicles travel between 63 miles per hour and 79 miles per hour.

Answer 1

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations from the mean
• 99.7% fall within three standard deviations from the mean

Given,

(Assume the data set has a​ bell-shaped distribution.)

Mean speed : = 71 miles per hour

standard deviation : = 4

percent of vehicles whose speeds are between 63 miles per hour and 79 miles per hour

63 is 71-2*4 (71-8=63) i.e  

79 is 71+2*4 (71+8) i.e

i.e. percent of vehicles whose speeds are between 63 miles per hour and 79 miles per hour = percent of vehicles whose speeds fall within two standard deviations from the mean

by the the Empirical Rule as stated above, percent of vehicles whose speeds fall within two standard deviations = 95%

the percent of vehicles whose speeds are between 63 miles per hour and 79 miles per hour = 95%