6.12 Project: Central Limit T

Introduction

In this project you will conduct a simple experiment by flipping a coin. Let x = number of heads in n coin flips. You need to record all your results, as you will be required to construct a frequency table as well as a histogram.

First Experiment

1. Flip a coin 10 times and record the number of heads.
2. Repeat step (1) 50 times. Each time record the number of heads. This means you will have collected 50 data points (50 times ten coin flips)
3. Construct a frequency table where you count the frequency of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 heads.
4. Construct a histogram of the frequency table.

Explain what type of distribution you see. Is the distribution skewed or normal?

Second Experiment

Now add up the number of heads for all the 50 trials.

1. Report the total number of heads.
2. 50 sets of 10 coin tosses, each, that means you flipped the coin 500 times. Theoretically the probability of heads at each individual toss is 1/2.
1. What is the expected mean number of heads?
2. What is the standard deviation?
3. How many number of heads would be considered usual/ordinary?

Recall lesson from Binomial Distribution as well as the fact that μ2σordinaryvaluesμ+2σ

$\mu -2\sigma \le ordinary\phantom{\rule{0ex}{0ex}}values\le \mu +2\sigma$

Analyze the “importance” of this graph. You need to keep this discussion civil. This is not a political debate. This analysis is strictly for the purpose in understanding how message are conveyed using statistical tools.

Response

Submit your response by direct text entry OR by uploading a PDF of your work.

The submission should contain:

• data containing the number of heads for each of the 50 trials of 10 coin flips
• frequency table summarizing the 50 collection of number of heads
• Histogram of the frequency table
• Sum of the total number of heads for the 500 coin flips
• Your calculations in answering questions of the second experiment

Your submission must be neat and legible. Be very detail oriented and submit a well written project. I will not accept work that looks as doodles or scratch paper work.

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