Purchase Solution

Understanding the Central Limit Theorem.

Not what you're looking for?

Ask Custom Question

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

Discuss the following: 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.

Purchase this Solution
Solution Summary

I demonstrate the properties of the central limit theorem (CLT) by conducting several dice rolling experiments with a web based java applet. Graphs of the process are included in the explanation.

Solution Preview

The response here does not include graphs and tables please see attachment.

There are multiple ways to understand the CLT in terms of dice. First you could imagine that you have a die. When you roll it there is a probability associated with the outcome. Namely,
Roll 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6
The mean of which is
1/6(1) + 1/6(2) + 1/6(3) + 1/6(4) + 1/6(5) + 1/6(6) = 3.5

Now imagine rolling the die 2 times or rolling 2 dice once (it doesn't matter in this case) and computed the mean of the dice. Possible outcomes are as follows:
(1,1) the mean of which is 1.
(1,3) the mean of which is 2.
(4,6) the mean of which is 5.

The CLT states that if we were to continue this experiment over and over and to compute the mean each time and to plot a histogram of our results (the means) they would have a normal distribution with a mean themselves approaching 3.5. So, we say that the mean of the sample means approaches the true population mean. ...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

View More Free Quizzes
Related BrainMass Solutions

  • Important information about Central Limit Theorem

    203351 Central Limit Theorem Proof What evidence do we have that the Central Limit Theorem is true? Why do so many of life's events share the same characteristics with Central Limit Theorem?

  • Central Limit Theorem of Mean

    200631 Central Limit Theorem of Mean What are the main characteristics/points of the Central Limit Theorem for a mean? Please see the attached file for complete solution. Work done with the help of equation writer may not print here.

  • normally distributed population has mean and standard deviation

    According to the central limit theorem, the mean of the sampling distribution is 40 The standard deviation of the sampling distribution is 12/sqrt(100) = 12/10 = 1.2 This brief solution implements the Central Limit Theorem and explains characteristics

  • Central Limit Theorum

    The Central Limit Theorem is indeed a very important and useful concept in statistics and plays a role in evaluations of the confidence level or hypothesis testing.

  • Central Limit Theorem

    204150 What evidence do we have that the Central Limit Theorem is true? What evidence do we have that the Central Limit Theorem is true? 1. What evidence do we have that the Central Limit Theorem is true?

  • Central Limit Theorem and Population Shape

    297562 Central Limit Theorem and Population Shape 1. State the main points of the Central Limit Theorem for a mean. 2. Why is population shape of concern when estimating a mean? What does sample size have to do with all?

  • Statistics: Probability density function, central limit theorem

    The expert examines the probability density function for central limit theorem.

  • Standard Deviation and The Central Limit Theorem

    Use the Central Limit Theorem. 1. a. Let x be the random variable having normal with mean 117 and standard deviation 6.4 P(X<119)= ?

  • Sample mean probabilities with the central limit theorem

    It describes the central limit theorem and gives details of the solution to this problem using the central limit theorem. This solution finds probabilities related to a sample mean by applying the central limit theorem.

  • Random Variable

    Answer: (a) Using Chebyshev's inequality; (b) the Central Limit Theorem

View More Related Solutions