There are 5 Great Lakes: Erie, Huron, Michigan, Ontario, and Superior. The following is a list of the water volumes of the Great Lakes (in cubic miles) in the order listed above.

116

850

1180

393

2900

a) What is the population mean? 

b) The following table shows all samples of size 3 from the population. The sampling distribution of the sample means of all samples of size 3 is a list of the means of each sample. What is the mean of sample 7?

Sample	Water Volumes
1	116, 850, 1180
2	116, 850, 393
3	116, 850, 2900
4	116, 1180, 393
5	116, 1180, 2900
6	116, 393, 2900
7	850,1180, 393
8	850, 1180, 2900
9	850, 393, 2900
10	1180, 393, 2900

c) What is the mean of the sampling distribution?

d) What observations can be made about the population and the sampling distribution?

i. The mean of the sampling distribution is (=, >, <) the mean of the population.

ii. The dispersion of the population is (wider than, narrower than, or the same width as) the dispersion of the sampling distribution of the sample means.

iii. The sampling distribution of the sample means tends to become (bell-shaped, positively skewed, or negatively skewed) and to approximate the normal distribution.