# Dice roll experiment

What is the mean number of rolls of a die before a 1 is observed? Roll a die until a 1 is observed. Repeat this process 30 times and answer the following questions.

1. Obtain a point estimate of the mean number of rolls of a die before a 1 is observed.

2. The population standard deviation for the number of rolls before a 1 is observed. Use this result to construct a 90% Z-interval for the mean number of rolls required before a 1 is observed.

3. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6? What proportion of the Z-intervals in the class included 6? How many did you expect to include 6?

4. Construct a 90% t-interval for the mean number of rolls required before a 1 is observed.

5. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6?

6. What proportion of the t-intervals in the class includes 6? How many did you expect to include 6?

7. Compare the Z-interval with the t-interval. Which has the smaller margin of error?

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#### Solution Summary

An experiment of rolling a dice a number of times to test a particular number (say 1) to appear on top.

Central Limit Theorem: Experiment for number of rolls of dice for normal distribution

Visit the following Web site Central Limit Theorem Applet and read what is posted: http://www.stat.sc.edu/~west/javahtml/CLT.html

You will choose from the pull down menu at the bottom of the page both the number of dice and the number of rolls at a time. When you "click" you will be virtually rolling your dice.

Complete the experiment using the following conditions. Note: You may need to click your Web browser's Refresh or Reload button to reset the experiment. Each time you repeat the experiment, keep track of how many clicks (rolls) it takes to produce a normal distribution:

1 die, 10 rolls at a time

1 die, 100 rolls at a time

1 die, 1000 rolls at a time

2 dice, 10 rolls at a time

2 dice, 100 rolls at a time

2 dice, 1000 rolls at a time

5 dice, 10 rolls at a time

5 dice, 100 rolls at a time

5 dice, 1000 rolls at a time

And because you are curious "if your computer allows" go ahead and try the experiment again with 10,000 rolls at a time

What does this experiment tell you about the Central Limit Theorem? What do you see happening as the number of die/dice being rolled changes from 1 to five? How might the number of rolls reveal an application of the Central Limit Theorem?

How is this information applicable to research in which you may be involved, including possible thesis/dissertation ideas you have?

With these thoughts in mind:

Post a report of how many clicks (rolls) it took under each condition to produce a normal distribution, a brief explanation of what conducting these experiments tells you about the Central Limit Theorem, and how this information may apply to research in which you may be involved.

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