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? (Round your answer to 1 decimal.)
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? (Round to 3 decimals.)
| 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? (Round your answer to 1 decimal.)
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.
a)) population mean=(116+850+1180+393+2900)/5=1087.8
b)
| (x1,x2) | mean(xbar) | |
| (116,850,1180) | 715.333 | |
| (116,850,393) | 453.000 | |
| (116,850,2900) | 1288.667 | |
| (116,1180,393) | 563.000 | |
| (116,1180,2900) | 1398.667 | |
| (116,393,2900) | 1136.333 | |
| (850,1180,393) | 807.667 | |
| (850,1180,2900) | 1643.333 | |
| (850,393,2900) | 1381.000 | |
| (1180,393,2900) | 1491.000 |
c)
mean of the sampling distribution=1087.80
d)i. The mean of the sampling distribution is = the mean of the population.
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