The Central Limit Theorem

Why should a normal model work for counts? Let’s use a binomial model to find the answer. If we have a computer to do the calculations, a binomial model makes it easy to find probabilities of the form

p(x)=P(xblue M&Ms in a bag)

for any choice of x from 0 to 58. It’s as if we opened many thousands of bags and counted the number of blue M&M’s in each. The model gives us a probability, the eventual relative frequency of the counts of blue candies in many bags.

Figure 2 shows the probabilities of different counts of blue M&M’s in bags of 58 pieces with n = 58 and p = 1/6.

A probability distribution graph of the number of blue candies in packages with 58 pieces. The graph is bell shaped.

Figure 2 Probability distribution of the number ...

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