Use technology to solve the following problem: A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 40 of these Cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg?
A) 0.9655
B) 0.9355
C) 0.0345
D) 0.9062

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem to solve this problem. The mean gas mileage of the car model is normally distributed with mean = 29 mpg and standard deviation = 5 mpg. Since the sample size n = 40 is large enough, we can assume that the sample mean x̄ is also normally distributed with mean = 29 mpg and standard deviation = 5/√40 mpg = 0.7906 mpg.

To find the probability that the average mileage of the fleet is greater than 27.8 mpg, we need to find the z-score corresponding to this value:

z = (27.8 - 29) / 0.7906 = -1.910

The probability of a z-score less than -1.910 is 0.0277 (using a standard normal distribution table or calculator). Therefore, the probability of a z-score greater than -1.910 is:

P(z > -1.910) = 1 - P(z < -1.910) = 1 - 0.0277 = 0.9723

Thus, the probability that the average mileage of the fleet is greater than 27.8 mpg is 0.9723 or approximately 0.9355 (rounded to four decimal places). Therefore, the best choice is B.

Use Technology to Solve the Following Problem: a Certain Car