Question

How do I solve the following equation? A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 3 mpg. a pizza delivery company buys 59 of these cars. what is the probability that the average mileage of the fleet is greater than 33.8 mpg?

Answer 1

The probability that the average mileage of the fleet is greater than 33.8 mpg is 0.695

Explanation:

The car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 3 mpg. We want to find the probability that the average mileage of the fleet is greater than 33.8 mpg, if a pizza delivery company buys 59 of these cars.

We calculate the z-score using:

`z=(x-\mu)/((\sigma)/(√(n) ) )`

We substitute
`\mu=34,\sigma=3,n=59,x=33.8`

`z=(33.8-34)/((3)/(√(59) ) )`

`z=-0.52`

From the standard normal distribution table, P(X>33.8)=0.695