Question

A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz and standard deviation 1.0 oz. We will randomly select n bags of cookies and weigh the contents of each bag selected.

Which of the following statements is true with respect to the sampling distribution of the sample mean, ¯xx¯?

According to the law of large numbers, if the sample size, n, increases, ¯xx¯ will tend to be closer to 15 ounces.

If the population standard deviation increases, the standard deviation of ¯xx¯ will increase.

If the sample size, n, increases, the standard deviation of will decrease.

All of the above.

Answer 1

Solution :

Given that,

mean = = 15

standard deviation = = 1.0

The following statements is true with respect to the sampling distribution of the sample mean, is

According to the law of large numbers, if the sample size, n, increases, will tend to be closer to 15 ounces.

If the population standard deviation increases, the standard deviation of will increase.

If the sample size, n, increases, the standard deviation of will decrease.

All of the above are correct .