Question

A new car that is a gas and electric powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.
a. the car travels more than 70 miles per gallon
b. the car travels less than 60 miles per gallon
c. the car travels between 55 and 70 miles per gallon

Answer 1

a.

$P(X>70)=P(Z>\frac{70-65}{4})=P(Z>1.25)=\\=1-P(Z<1.25)=0.1056.$

b. $P(X<60)=P(Z<\frac{60-65}{4})=P(Z<-1.25)=0.1056.$

c.

$P(55<X<70)=P(\frac{55-65}{4}<Z<\frac{70-65}{4})=P(-2.5<Z<1.25)=\\=P(Z<1.25)-P(Z<-2.5)=0.8882.$