A sample size of three is drawn from the set 5, 6,8,12 and 20.

Question

A. How many possible samples can be drawn?

B. Construct the sampling distribution of sample means.

C. Solve the variance and the standard deviation of the sampling, distribution of the sample means.

Answer 1

Part A:

The first thing you need to do is answer these two questions:

1) Does order matter? for example, is {1,2) the same or different than (2, 1)?

2) Are you replacing the number after you draw it? In other words, can you draw the same number multiple times?

After you answer these 2 questions, you will know whether to use the formula for a combination (order doesn't matter) or a permutation (order matters).

The formula for a permutation is: n!/(n-r)!, where n is the number of things to choose from, and we choose r of them.

The formula for a combination is:n!/(n-r)! r!, where n is the number of things to chose from, and we choose r of them, but since order doesn't matter, we divide by the redundancies (that what the extra r! in the denominator is doing!

Now, all you need to do is figure out the answer to the 2 questions & calculate accordingly!