the average miles per gallon of a particular automobile model are approximately normally distributed with a…

the average miles per gallon of a particular automobile model are approximately normally distributed with a given mean $mu = 43.8$ miles per gallon and standard deviation $sigma = 5.1$ miles per gallon. what percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?\n68%\n75%\n95%\n100%

the average miles per gallon of a particular automobile model are approximately normally distributed with a given mean $mu = 43.8$ miles per gallon and standard deviation $sigma = 5.1$ miles per gallon. what percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?\n68%\n75%\n95%\n100%

Answer

Answer:

A. 68%

Explanation:

Step1: Calculate z - scores

For (x_1 = 38.7), (z_1=\frac{x_1-\mu}{\sigma}=\frac{38.7 - 43.8}{5.1}=\frac{- 5.1}{5.1}=-1) For (x_2 = 48.9), (z_2=\frac{x_2-\mu}{\sigma}=\frac{48.9 - 43.8}{5.1}=\frac{5.1}{5.1}=1)

Step2: Use the empirical rule

The empirical rule for a normal - distribution states that approximately 68% of the data lies within 1 standard deviation of the mean. Since (z_1=-1) and (z_2 = 1), the percentage of automobiles with an average miles per gallon between 38.7 and 48.9 is approximately 68%.