Toss a coin 40 times and record the number of heads. Develop a frequency distribution of the number of heads from the results of your experiment. Does this distribution seem to approximate the normal distribution? Is it skewed? What is important about the number of tosses – 40 in this case?
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To develop a frequency distribution of the number of heads, we need to conduct the coin toss experiment and record the results. Here is an example of possible outcomes:
HHHTHTTHHHTTTTHHHTTHHTTTHHTHHHHHTTTHHTTHHHTTTTHHTHTTHHHTTTHHHTTTH
From these 40 tosses, we count the number of heads:
HHHTHTTHHHTTTTHHHTTHHTTTHHTHHHHHTTTHHTTHHHTTTTHHTHTTHHHTTTHHHTTTH
H H H T H H T T H H T T H T T H H H H H T T H H T T H H T T H H H
Now we can create a frequency distribution table:
Number of Heads | Frequency
----------------|----------
0 | 0
1 | 1
2 | 4
3 | 6
4 | 5
5 | 7
6 | 5
7 | 5
8 | 3
9 | 2
10 | 2
This distribution does not seem to approximate the normal distribution. From the data, it appears that there are more outcomes with higher or lower numbers of heads, meaning it is skewed.
The number of tosses – 40 in this case – is important because as the number of tosses increases, the distribution will tend to approximate the normal distribution. This follows the concept of the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution. Therefore, with a larger number of tosses, the frequency distribution of the number of heads is more likely to approximate the normal distribution.
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