5 dice or an online dice rolling simulator which can be found

## Be Prepared For The Toughest Questions

### Practice Problems

5 dice or an online dice rolling simulator which can be found

Student Learning Outcomes: Students will use their results from a dice rolling experiment to explore the Central Limit Theorem.

Materials: 5 dice or an online dice rolling simulator which can be found at https://www.random.org/dice/

Procedure: For one die, students will roll and record the face number. For multiple dice, students will roll and each time record the average of the dice faces

Rolling 1 Die:

Roll a single die 20 times and record the tally in the table below.

Use your data to make a frequency histogram for your results from rolling 1 die. There should be 6 bins, each of which correspond to the 6 die faces. Label and scale your axes.

Calculate the mean bar x and standard deviation sx.

bar x =

sx =

Rolling Multiple Dice:

Averaging the Faces.

(a) Roll 2 of the dice and average the face numbers. Put a tally in the 2 dice column for the average that you got. Do this 20 times.

(b) Roll 5 of the dice and average the face numbers. Put a tally in the 5 dice column for the average that you got. Do this 20 times.

Make 2 more frequency histograms. One for averaging 2 dice, and the second for averaging 5 dice. You should have 11 bins for the 2 dice histogram and 26 bins for 5 dice histogram (same as the face average column in frequency table) on the horizontal axis. Label your axes. Also, use your calculator to find the mean and standard deviation for each case.

Note: To find the mean and standard deviation for each case (n = 2 and n = 5) you will be putting the face averages in a calculator list. You will have 20 numbers in your list for each case.

Summary Questions for Dice Experiment

(1) How can we describe the shape of the 3 histograms? How do the histograms change as we average more dice?

(2) Compare the sample means x for each case. Do the sample means seem to approach a number as we average more dice?

(3) Compare the standard deviations sx for each case. What do you notice about the standard deviations as we average more dice?

Our dice experiment used experimental probability to explore the Central Limit Theorem will be studied in depth in Chapter 7. We will go over these results on the first day of lecture for Chapter 7.

Hint
Statistics The central limit theorem is a concept in probability theory. Accordingly, given a large sample size to represent a population whose variance level is finite, the mean of all samples will be almost equivalent to the mean of the whole population....

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