Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 50 miles and a standard deviation of 6 miles. Find the probability of the following events. Use Excel to obtain more accuracy.

A. The car travels more than 53 miles per gallon. Probability =

B. The car travels less than 47 miles per gallon. Probability =

C. The car travels between 44 and 57 miles per gallon. Probability =

Answer 1

Given mean = 50 miles SD = 6 miles

A) Probability that the car travels more than 53 miles

Z score calculation = (53-50)/6 = 0.5

p(Z>0.5) = 1-0.6915 = 0.3085

B) Probability that car travels less than 47 miles

z score calculation = (47-50)/6 = -0.5

p(Z<-0.5) = 0.3085

C) p(44<x<57)

z score for 44 gallons = 44-50/6 = -1

z score for 57 gallons = 57-50/6 = 1.167

p(z<-1) = 0.1587

p(z<1.167) = 0.8790

===>p(44<x<57)= 0.8790-0.1587 = 0.7203