Question

The Environmental Protection Agency (EPA) rates the mean highway gas mileage of the 2017 Chevrolet Sonic to be 28 miles per gallon. Assume the standard deviation is 3 miles per gallon. A rental company bought 60 of these cars.

a. What is the probability that the average mileage of the fleet is greater than 27.5 miles per gallon?

b. What is the probability that the average mileage of the fleet is between 27 and 27.8 miles per gallon?

c. What mileages would be considered unusual? (Recall unusual is the top and bottom 5%)

Answer 1

(A) using normalcdf

setting lower = 27.5

upper = 9999

mean = 28

standard deviation = 3/sqrt(60)

=normalcdf(lower, upper, mean, sd)

=normalcdf(27.5,9999,28,3/sqrt(60))

= 0.9016

(B)

using normalcdf

setting lower = 27

upper = 27.8

mean = 28

standard deviation = 3/sqrt(60)

=normalcdf(lower, upper, mean, sd)

=normalcdf(27,27.8,28,3/sqrt(60))

= 0.2979

(C) lower value = NORMINV(probability, mean, sd)

setting probability = 0.05

mean = 28 and sd = 3/sqrt(60)

=NORMINV(0.05,28,3/sqrt(60))

= 27.36

and

upper value = NORMINV(probability, mean, sd)

setting probability = 0.95

mean = 28 and sd = 3/sqrt(60)

=NORMINV(0.95,28,3/sqrt(60))

= 28.64