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 distribution of 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.

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Quizplus · Accepted Answer

This is because 14 and 16 are one standard deviation away from the population mean of 15. According to the empirical rule of Normal distributions, approximately 68.26% of a Normal distribution falls within one standard deviation of the mean. Since the distribution is assumed to be symmetric, we can use the empirical rule (68-95-99.7) to estimate the probability of the sample mean falling between 14 and 16 gallons. The interval of 14 to 16 gallons is one standard deviation away from the population mean of 15 gallons. Therefore, according to the empirical rule, there is approximately a 68.26% chance that the sample mean will fall within this interval.

If the Amount of Gasoline Purchased Per Car at a Large