An automobile manufacturer introduces a new model that averages 26.0 miles per g

Question

An automobile manufacturer introduces a new model that averages 26.0 miles per gallon in the city. A person who plans to purchase one of these new cars wrote the manufacturer for the details of the tests, and found out that the standard deviation is 3.8 miles per gallon. Assume that in-city mileage is approximately normally distributed. ____% of the automobiles have between 18 and 21 miles per gallon. Round the z-score to two decimal places if needed. Round your answer to two decimal places. Do not include the % sign in your answer.

Explanation / Answer

Mean =26

S.D = 3.8

Z score at x=18

Z = (X - ?) / ?
Z = (18 - 26) / 3.8

Z = -2.10526

Z = (X - ?) / ?
Z = (21 - 26) / 3.8

Z = -1.31579

P( 18<X<21) = p( -2.10526<Z<-1.31579 )

From z score table

P( 18<X<21) = p( -2.10526<Z<-1.31579 )= 0.0765

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