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Part 1: Introductory Information

The following shows the probability distribution for rolling a six-sided die and the Expected Value. The random variable in this case is the number showing when the rolling a six-sided die.

1
2
3
4
5
6

Therefore, the expected value of the random variable,x, is3.5.

Since the probability remains the same for each random variable,x, the probability distribution of thexis a uniform distribution.

Part 2: Your task

Step 1: Roll a six-sided die 40 times and record the results. Here are mine.

1	6	2	5	6	5	3	4
6	2	2	5	6	6	2	4
4	4	4	2	1	4	3	5
2	2	1	5	6	2	6	5
1	4	4	4	6	1	4	3

Step 2: Calculate the sample mean. Round to the nearest tenths place. Here is my result.

We now have a sample (n = 40) where the sample mean,(rounded to the nearest tenths place)

Step 3: Repeat steps 1 and 2 again and show your results.

6	6	2	1	6	5	3	5
2	6	5	2	3	1	6	1
2	2	6	1	5	5	1	2
3	5	5	4	3	3	1	5
1	2	1	6	4	2	1	6

Step 4: Find the mean of the two sample means.

mean of the sample means =

Step 4: Answer the following questions?

1. Was the sample mean the same for both samples?
2. Were the sample means close to each other?
3. The mean is another term for expected value. How did your sample means compare to the expected value 3.5?
4. How does the mean of your sample means (sampling distribution) compare to the expected value 3.5?