A certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 35 of these cars. What is the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg?
A)0.2310
B)0.6517
C)0.4207
D)0.7690

Question

Quizplus · Accepted Answer

The correct answer is A.The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 35, which is large enough to apply the central limit theorem.The mean of the sample mean distribution will be equal to the population mean, which is 31 mpg. The standard deviation of the sample mean distribution will be equal to the population standard deviation divided by the square root of the sample size, which is 3 mpg / sqrt(35) = 0.548 mpg.Therefore, the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg is equal to the probability that the sample mean is between 30.9 and 31.2 mpg. This probability can be calculated using the normal distribution with a mean of 31 mpg and a standard deviation of 0.548 mpg. Using a standard normal distribution table, we find that the probability is 0.2310.

A Certain Car Model Has a Mean Gas Mileage of 31