Statistics for Business: Decision Making and Analysis, 3rd Edition

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

$$p\left(x\right)=P\left(x\hspace{0.17em}\text{blue} \text{M}\&\text{M}\prime \text{s} \text{in} \text{a} \text{bag}\right)$$

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.

Figure 2 Probability distribution of the number ...