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Normal approximation to the binomial distribution

A. Tossing a Coin

Simulate 6 independent tosses of a fair coin. Repeat the procedure to get 200 sets of 6 coin tosses. (That's 1200 total tosses.) List the results.

Explain carefully your method of simulating the tosses, whether it involves a computer, a table of random digits, or even flipping several coins at once. Address the issues of fairness, independence, and randomness. You are encouraged to find a clever way to generate the data.
Let X denote the number of heads in a set of 6 tosses. Thus the sample space for X is {0, 1, 2, 3, 4, 5, 6}. From your data above, make a histogram of the observed values of X. There are 200 cases.
From the data, compute the relative frequency of cases with X > 2.
In theory, what is the probability that X > 2 in any given case? Remember, we assume that the chance of heads on any toss is p = .5 and that the toss outcomes are independent.

Do you find that this agrees with the data, within reason?
Suppose just for now that p = .525. For this problem first compute the total number of heads in all 1,200 tosses. (Use your histogram.)

Next let n = 1200 and use the normal approximation to the binomial distribution B(1200, .525) to find the probability of observing no more than the number of heads you did.


Solution Summary

The solution gives the details of normal approximation to the binomial distribution.