Outline

Discuss the Binomial Distribution

Discuss conditions under which we can use the normal approximation to the binomial distribution

Work on problems using the binomial distribution

When a variable is measured on a scale consisting of exactly two categories, the resulting data are called binomial.

The question of interest is the number of times each category occurs in a series of trials, or in a sample of individuals.

E.g. What is the probability of having more than 30 females in a sample of 50 college freshmen?

The normal distribution serves also as a model for computing probabilities with binomial data.

The binomial distribution shows the probability associated with each value of x, from x = 0, to x = n.

The categories are identified as A and b.

The probabilities associated with each are identified as

p =  p(A) = probability of A

q = p (B) = probability of B

p + q = 1

n = the number of individuals or observations in the sample.

Variable x refers to the number of times category A occurs in the sample.

The binomial distribution tends toward a normal shape, when n is large.

The binomial will be a nearly perfect normal distribution when pn and qn are both equal to or greater than 10.

In this case, the binomial distribution will have the following parameters:

Mean = m = np

SD = s = square root of npq

Under these conditions we can compute probability values directly from z-scores and the unit normal table.