Sanderson M. Smith

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THE BINOMIAL SETTING

(MINI-PROJECT BY ANNE)

Anne's chart provides describes a description of the **binomial setting:**

- Each observation falls into one of just two categories, which we will call success and failure.
- There are a fixed number, n, of observations.
- The n observations are independent of each other.
- The probability of success, p, is the same for each observation.

If k = 0,1,2,3,..., n, then

Probability (k successes) =

_{n}C_{k}p^{k}(1-p)^{n-k}

Anne provides an example problem:

At Herky, Inc., a company with a large number of employees, approximately 25% of the workers are vegetarians. If a group of 12 Herky, Inc. employees is randomly chosen, what is the probability that the group contains exactly 5 vegetarians.

Anne's displayed answer is

_{12}C_{5}(.25)^{5}(.75)^{7}= 0.1032, or about 10%.Note: Using the TI-83, one can calculate

binompdf(12,.25,5)= .1032.

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