Question

An automobile manufacturer introduces a new model that averages 27 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 miles per gallon. Assume that in-city mileage is approximately normally distributed (use z score table)

a) What percentage of the time is the car averaging less than 20 miles per gallon for in-city driving.

b) What percentage of the time is the car averaging between 25 and 29 miles per gallon for in- city driving?

Answer 1

Solution:-

Mean = 27, S.D = 3

a) The percentage of the time is the car averaging less than 20 miles per gallon for in-city driving is 0.98%.

x = 20

By applying normal distribution:-

z = - 2.333

P(z < - 2.33) = 0.0098

P(z < - 2.33) = 0.98 %

b) The percentage of the time is the car averaging between 25 and 29 miles per gallon for in- city driving is 49.52%.

x₁ = 25

x₂ = 29

By applying normal distribution:-

z₁ = - 0.667

z₂ = 0.667

P( - 0.667 < z < 0.667) = P(z > - 0.667) - P(z > 0.667)

P( - 0.667 < z < 0.667) = 0.7476 - 0.2524

P( - 0.667 < z < 0.667) = 0.4952

P( - 0.667 < z < 0.667) = 49.52 %