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 a random
sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will
be between 14 and 16 gallons.

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal with a mean of 15 gallons and a standard deviation of 0.5 gallons (4/√64). Using the empirical rule (68-95-99.7 rule), about 95.44% of the sample means will fall within two standard deviations (1 gallon) of the mean, i.e., between 14 and 16 gallons.

True or False: If the Amount of Gasoline Purchased Per