Question

The typical gas mileage for a type of car is normally distributed with a mean of 48 mpg and a standard deviation of 6 mpg

1.) What percent of the cars will get between 54 and 66 mpg according to the empirical rule? Explain in statistical detail.

(My answer was 16% but my instructor says it is 15.85% - I do not understand the rationale). Thank you.

Answer 1

Answer

Given that mean = 48 and standard deviation = 6

we can write it as

54 = 48 + 6 or 1 standard deviation above the mean

similarly, 66 = 48 + 3*6 or 3 standard deviation above the mean

using the empirical rule, we know that only 13.5% data fall within

and only 2.35% data fall within

Therefore, total percent of data between = 13.5% + 2.35% = 15.85%

So, there is 15.85% of data between 54 mpg and 66 mpg