Question

Construct a sampling distribution of sample mean and answer the questions on
your answer sheet.
Samples of 3 cards are drawn from a population of five cards numbered from 1-5.
1. How many are the possible outcomes?
2. What are the possible means?
3. What is the probability of getting 4 as a mean?
4. What is the probability of getting 2 as a mean?
5. What is the probability of getting 3.33 as a mean?

Answer 1

N=5

n=3

Without replacement

1. Number of outcomes $= \frac{N!}{n!(N-n)!}$

$= \frac{5!}{3!(5-3)!} = \frac{4 \times 5}{2} = 10$

2.

The sampling distribution of sample mean

3. P(Mean=4) $= \frac{1}{10}=0.1$

4. P(Mean = 2) $= \frac{1}{10}=0.1$

5. P(Mean=3.33) $= \frac{2}{10}=0.2$