1. Normal Approximations to the Binomial Distribution
Section 4
Normal Approximations to the Binomial Distribution

2. Example
A sociologist conducted interviews with 16 registered voters. Assume that half the voters on the list are Democrats.
Let x = the number of Democrats selected
n = 16
p = ½ p(x) =
q = ½

3. For approximating a binomial probability with a normal probability
A binomial random variable x may be thought of as having an approximately normal distribution if n is sufficiently large.
Note: n is sufficiently large if np and
nq are at least 5.
When approximating a binomial probability with a normal probability, use the continuity correction.

4. Example
Find the probability that between 30 and 35 of the next 50 births at a particular hospital will be boys.