Acertain 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?

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

0.0796

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