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 a random sample of 4 cars is selected,there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

Question

Quizplus · Accepted Answer

To find the probability that the sample mean falls between 13 and 17 gallons, we need to calculate the standard error of the mean:

standard error = standard deviation / sqrt(sample size) = 4 / sqrt(4) = 2

Then, we need to compute the z-scores associated with the sample mean of 13 gallons and the sample mean of 17 gallons:

z(13) = (13 - 15) / 2 = -1
z(17) = (17 - 15) / 2 = 1

From a standard normal distribution table, we can find that the probability of getting a z-score between -1 and 1 is approximately 0.6827. However, this is the probability of obtaining a sample mean within that range if we were to take an infinite number of samples of size 4 from the population. We cannot say anything about the probability of obtaining a sample mean within that range for a single sample of size 4. Therefore, the statement is false.

If the Amount of Gasoline Purchased Per Car at a Large