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

Answer:

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

Step-by-step 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:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }$

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

$z=\frac{33.8-34}{\frac{3}{\sqrt{59} } }$

$z=-0.52$

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