If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 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.

Question

Quizplus · Accepted Answer

This statement is true. Given a normal population with known mean and standard deviation, the distribution of sample means will also be normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. The confidence interval for the population mean can be calculated using the formula:

sample mean +/- (critical value) * (population standard deviation / sqrt(sample size))

For a 95% confidence interval, the critical value is approximately 1.96. Plugging in the given values, we get:

$15 +/- 1.96 * ($4 / sqrt(64))
$15 +/- $0.98

This means that there is a 95% chance that the sample mean will fall between $14.02 and $15.98, which includes the range of $14 to $16. Therefore, the statement is true.

If the Amount of Gasoline Purchased Per Car at a Large