Question

An economist is studying the average yearly household income in Alaska. They know that the average yearly income in the United States is normally distributed with a mean of $59, 040, and a standard deviation of $14, 530. If a sample of 150 Alaskan families is selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

Select all that apply:
a. δx = $1,186.37
b. δx = $14,530
c. δx = $96.87
d. µx = $59,040
e. µx = $4,820.60
f. µx = $393.60

Answer 1

The expected mean of the sampling distribution is $59,040 and the standard deviation of the sampling distribution is approximately $1,186.37.

Step-by-step explanation:

To find the expected mean of the sampling distribution, we use the fact that the mean of the sampling distribution is equal to the mean of the population, which is $59,040. Therefore, the expected mean of the sampling distribution is µx = $59,040.

To find the standard deviation of the sampling distribution, we use the fact that the standard deviation of the sampling distribution is equal to the standard deviation of the population divided by the square root of the sample size. The standard deviation of the sampling distribution is given by the formula:

δx = σ / √n, where σ is the standard deviation of the population and n is the sample size. Plugging in the values, we get:

δx = $14,530 / √150 ≈ $1,186.37.