Question

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with a mean of 8.2 minutes and standard deviation of 1.5 minutes. Suppose a random sample of n customers is taken. Which of the following statements is true about the sampling distribution of the sample mean?

a) The sampling distribution will have a mean of 8.2 minutes.
b) The sampling distribution will have a standard deviation of 1.5 minutes.
c) The shape of the sampling distribution will be normal regardless of the sample size.
d) The standard deviation of the sampling distribution decreases as the sample size increases.

Answer 1

The correct statements regarding the sampling distribution of the sample mean for airport check-in wait times are that it will have a mean of 8.2 minutes, and the standard deviation of the sampling distribution decreases as the sample size increases.

Step-by-step explanation:

The question pertains to the properties of the sampling distribution of the sample mean for the time customers spend at an airport check-in counter. The correct statement about the sampling distribution of the sample mean is a) The sampling distribution will have a mean of 8.2 minutes. This statement is based on the Central Limit Theorem, which indicates that the sampling distribution of the sample mean will have the same mean as the population mean if the sample size is sufficiently large. The standard deviation of the sampling distribution, also known as the standard error, is indeed affected by the sample size and is given by the population standard deviation divided by the square root of the sample size (b). Therefore, statement d) The standard deviation of the sampling distribution decreases as the sample size increases is also true.