Answer to Question #248393 in Statistics and Probability for Yara

Question

New car that is a gas and electric powered highbred has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 50 miles in the standard deviation of 8 miles. Find the probability of the following events.

A. The car travels more than 55 miles per gallon

B. The car travels less than 47 miles per gallon

C. The car travels between 47 and 58 miles per gallon

Answer 1

A. $P(X>55)=P(Z>\frac{55-50}{8})=P(Z>0.63)=0.2643.$

B. $P(X<47)=P(Z<\frac{47-50}{8})=P(Z<-0.38)=0.3520.$

C. $P(47<Z<58)=P(\frac{47-50}{8}<Z<\frac{58-50}{8})=P(-0.38<Z<1)=0.4893.$