4.2 Binomial Distributions

• Important Concepts– Binomial Experiment– Binomial Probability Formula– Mean (or Expected Value), Variance, and

Standard Deviation of a Binomial Random Variable

4.2 Binomial Distributions

• So what exactly is a Binomial Experiment?– A probability experiment that satisfies the

following four conditions:• The experiment is repeated for a fixed number of

trials, where each trial is independent of the other trials.

• There are only two possible outcomes of interest for each trial (either a success, S, or a failure, F).

• The probability of a success is the same for each trial.• The random variable X counts the number of

successful trials.

4.2 Binomial Distributions

• #16 p. 211 (Childhood Obesity)– We’ll start with 3 U.S. adults instead of 6.

• Binomial Probability Formula

valid for x = 0,1,2,…,n

• #16 p. 211 Let’s work with all 6 adults this time.

( ) x n xP X x nCx p q

4.2 Binomial Distributions

• Mean, Variance, and Standard Deviation of a Binomial Random Variable:– Good news! We do not have to build tables

like we did in the last section to find these parameters. We can use formulas!

2

np

npq

npq

4.2 Binomial Distributions

• #29 p. 212 (Life on Mars)– We could also construct a probability

histogram for this binomial random variable. Since p < 0.50, we would expect the graph to be skewed to the right.