Question

A certain car model has a mean gas mileage of 28 miles per gallon with a standard deviation 5 mpg. Suppose nothing is known about the distribution of gas mileage. A pizza delivery company buys 37 of these cars. What is the probability that the average mileage of the fleet us between 27.2 and 28.8 mpg?

Answer 1

the probability that the average mileage of the fleet us between 27.2 and 28.8  will be:
27.2<x<28.8
this will be:
P(x<28.8)-P(x<27.2)
To evaluate this we use the z-score formula:
P(x<28.2)=P(z<Z)
Z=(x-μ)/σ
μ-mean
σ-standard deviation
thus
z=(28.2-28)/5=0.04
thus
P(x<28.2)=0.5160

p(x<27.2
z=(27.2-8)/5=-0.16
P(z<-0.16)=0.4364
thus
P(x<28.8)-P(x<27.2)=0.5160-0.4364=0.0796

Answer: 0.0796