A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 4 mpg. A pizza delivery company buys 54 of these cars. What is the probability that the average Mileage of the fleet is between 33.3 and 34.3 mpg?
A) 0.6103
B) 0.0985
C) 0.7088
D) 0.3897

Question

Quizplus · Accepted Answer

The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. In this case, the population mean is 34 mpg and the population standard deviation is 4 mpg. The sample size is 54, which is large enough to invoke the central limit theorem.The probability that the average mileage of the fleet is between 33.3 and 34.3 mpg is the area under the normal curve between z-scores of -0.25 and 0.25. This area is approximately 0.6103.

A Certain Car Model Has a Mean Gas Mileage of 34