Question

A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with standard deviation of 3mpg . A delivery company buys 49 of these cars. What is the probability that the average mileage of the fleet is greater than 28.8 mpg?

Answer 1

0.6808

Explanation:

First, find the standard deviation of the sample.

s = σ / √n

s = 3 / √49

s = 0.429

Next, find the z-score.

z = (x − μ) / s

z = (28.8 − 29) / 0.429

z = -0.467

Use a calculator or z-score table to find the probability.

Using a table:

P(x > -0.47) = 1 − 0.3192 = 0.6808

Using a calculator:

P(x > -0.467) = 0.6796