1. 4.2 Binomial Distributions
Important Concepts
Binomial Experiment
Binomial Probability Formula
Mean (or Expected Value), Variance, and Standard Deviation of a Binomial Random Variable

2. 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.

3. 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.

4. 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!

5. 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.