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 given statement is related to the central limit theorem which states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population distribution, as long as the sample size is sufficiently large. The sample mean has a standard error of (standard deviation of population) / sqrt(sample size) = 4 / sqrt(16) = 1. Therefore, the interval of (14, 16) is 1 standard error away from the population mean of 15. By the empirical rule, there is approximately a 68.26% chance that the sample mean falls within 1 standard error of the population mean. Therefore, the given statement is true.

If the Amount of Gasoline Purchased Per Car at a Large