Question

the average gas mileage of a certain model car is 2.6 miles per.gallon. if gas mileage are normally distributed with standard deviation of 0.15 miles per gallon find the probability that a car has a gas mileage of between 25.8 and 26.2 miles per gallon

Answer 1

Average gas mileage of a certain model car = = 26 mpg

standard deviation of gas mileage of certain model car = = 0.15 mpg

Here if x is the gas mileage of a random car then x follows the normal distribution x ~ N(26 mpg, 0.15 mpg)

Here we have to find

Pr(25.8 mpg < x < 26.2 mpg) = Pr(x < 26.2 mpg ; 26 mpg; 0.15 mpg) - Pr(x < 25.8 mpg ; 26 mpg ; 0.15 mpg)

Z₂ = (26.2 - 26)/0.15 = 0.2/0.15 = 1.333

Z₁ = (25.8 - 26)/0.15 = -1.333

Here we will use the normsdist function of excel or normcdf function of TI-83 calculator or Z table

Pr(25.8 mpg < x < 26.2 mpg) = Pr(x < 26.2 mpg ; 26 mpg; 0.15 mpg) - Pr(x < 25.8 mpg ; 26 mpg ; 0.15 mpg)

= Pr(Z < 1.3333) - Pr(Z < -1.3333)

= NORMSDIST(1.3333) - NORMSDIST(-1.3333)

= 0.9088 - 0.0912 = 0.8176