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
P( X  x)   nCx  p q
x
n x
valid for x = 0,1,2,…,n
• #16 p. 211 Let’s work with all 6 adults this time.
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!
  np
 2  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.