Binomial vs. Geometric

1
Binomial vs. Geometric

• Chapter 8
• Binomial and Geometric Distributions

2
Binomial vs. Geometric
The Binomial Setting The Geometric Setting

• Each observation falls into
• one of two categories.

1. Each observation falls into one of two
categories.

• The probability of success
• is the same for each
• observation.

2. The probability of success is the same
for each observation.

• The observations are all
• independent.

• The observations are all
• independent.

• There is a fixed number n
• of observations.

4. The variable of interest is the number of
trials required to obtain the 1st success.
3
Are Random Variables and Binomial Distributions
Linked?
X number of people who purchase electric hot tub
X
0 1 2 3
.288
P(X)
.216
.432
.064
(.6)(.6)(.6)
GGG
EEG GEE EGE
(.4)(.4)(.6) (.6)(.4)(.4) (.4)(.6)(.4)
EGG GEG GGE
(.4)(.6)(.6) (.6)(.4)(.6) (.6)(.6)(.4)
EEE
(.4)(.4)(.4)
4
Combinations
Formula
Practice
5
Developing the Formula
Outcomes
Probability
Rewritten
OcOcOc
OOcOc
OcOOc
OcOcO
OOOc
OOcO
OcOO
OOO
6
Developing the Formula
n of observations p probablity of success k
given value of variable
Rewritten
7
Working with probability distributions

• State the distribution to be used
• Define the variable
• State important numbers
• Binomial n p
• Geometric p

8
Twenty-five percent of the customers entering a
grocery store between 5 p.m. and 7 p.m. use an
express checkout. Consider five randomly
selected customers, and let X denote the number
among the five who use the express checkout.
binomial
n 5 p .25
X of people use express
9
What is the probability that two used express
checkout?
binomial
n 5 p .25
X of people use express
10
What is the probability that at least four used
express checkout?
binomial
n 5 p .25
X of people use express
11
Do you believe your children will have a higher
standard of living than you have? This question
was asked to a national sample of American adults
with children in a Time/CNN poll (1/29,96).
Assume that the true percentage of all American
adults who believe their children will have a
higher standard of living is .60. Let X represent
the number who believe their children will have a
higher standard of livingfrom a random sample of
8 American adults.
binomial
n 8 p .60
X of people who believe
12
Interpret P(X 3) and find the numerical answer.
binomial
n 8 p .60
X of people who believe
The probability that 3 of the people from the
random sample of 8 believe their children
will have a higher standard of living.
13
Find the probability that none of the parents
believe their children will have a higher
standard.
binomial
n 8 p .60
X of people who believe