True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons and it is assumed
that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26%
chance that a random sample of 16 cars will have a sample mean between 14 and 16 gallons.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. In this case, the sample size is 16, which is large enough to apply the Central Limit Theorem. Therefore, the sampling distribution of the sample mean will be approximately normal with a mean of 15 gallons and a standard deviation of 4/sqrt(16) = 1 gallon. Using the standard normal distribution, we can find that the probability of a sample mean between 14 and 16 gallons is approximately 68.26%.

True or False: If the Amount of Gasoline Purchased Per