The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean mc024-1.jpg = 43.8 miles per gallon and standard deviation mc024-2.jpg = 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?
a.68%
b.75%
c.95%
d.100%

The correct answer is option(a).

Explanation:

= Standrad deviation

= Mean of the observations

Using standard Z-table: for and

For , the value from Z table = 0.1587

For , the value from Z table = 0.8413

Percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon:

=0.8413 - 0.1587 = 0.6826 = 68.26 %

Hence, the correct answer option(a).

i don't understand. explain it clearly