Solution:
Explanation:
(a)
The possible samples with their means is given below:
Samples | Sample means |
1,1 | 1 |
1,2 | 1.5 |
1,3 | 2 |
1,4 | 2.5 |
2,1 | 1.5 |
2,2 | 2 |
2,3 | 2.5 |
2,4 | 3 |
3,1 | 2 |
3,2 | 2.5 |
3,3 | 3 |
3,4 | 3.5 |
4,1 | 2.5 |
4,2 | 3 |
4,3 | 3.5 |
4,4 | 4 |
Therefore, the sampling distribution of means is:
c)
The possible samples with their ranges are:
Samples | Range |
1,1 | 0 |
1,2 | 1 |
1,3 | 2 |
1,4 | 3 |
2,1 | 1 |
2,2 | 0 |
2,3 | 1 |
2,4 | 2 |
3,1 | 2 |
3,2 | 1 |
3,3 | 0 |
3,4 | 1 |
4,1 | 3 |
4,2 | 2 |
4,3 | 1 |
4,4 | 0 |
Therefore, the sampling distribution of Ranges is:
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