1. The Binomial and Geometric Distribution
Chapter 8
The Binomial and Geometric Distribution

2. Activity 8A
Students close your eyes and imagine this happening to you.
Now, Number your paper from 1 to 10. There are five choices for each question: A,B,C,D,E
Select an answer to each question.

3. Answers (score your own paper)
3. B
4. D
5. C
6. A
7. A
8. D
9. E
10. C

4. Cont. Activity 8A
Answer questions 3 and 4. You have 15 minutes. When finished write in classwork and save in folder.
Class discussion on findings.

5. 8.1 The Binomial Distribution
Interested in two outcomes in each trial, the result is either a success or a failure. (more interested in the number of successes.

6. Binomial Setting
1. Each observation falls into one of just two categories, we call "success" or "failure".
2. There is a fixed number n of observations.
3. The n observations are all independent. Knowing the result of one observation tells you nothing about the other observations.
4. The probability of success, call it p, is the same for each observation.

7. Binomial Distribution
Probability distribution of X
X = the number of successes
(Binomial Random Variable)
Parameters n and p
n = number of observations
p = probability of success on one observation
The possible values of X are the whole numbers from 0 to n. B(n,p)

8. Examples Student A please read example 8.1
Student B please read example 8.2

9. Sampling Distribution of a Count
Choose an SRS of size n from a population with proportion p of success.
when the population is much larger than the sample, the count X of successes in the sample has approximately the binomial distribution with parameters n and p

10. Binomial Formulas B(5, 0.25) Find P(X=2) thats 2 success, 3 fails.
(.25)(.25)(.75)(.75)(.75)
There are 10 ways to write SSFFF, SFSFS...
So, P(X=2) = 10(.25)2(.75)3 =

11. Binomial Coefficient
The number of arranging k successes among n observations is given by
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12. Binomial Probability
If X has the binomial distribution with n observations and probability p of success on each observation, the possible values of X are 0,1,2...,n. if k is any one of those values,
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13. Calculator Probability Distribution Function binompdf(n,p,X)
Cumulative Binomial Probability
binomcdf(n,p,X)

14. Mean and Standard Diviation
µ = np
σ = √np(1-p)

15. normal approximation for binomial distribution
when n is large the distribution of X is Approximately Normal, N(µ,σ)