The Binomial and Geometric Distribution Chapter 8 The Binomial and Geometric Distribution

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.

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

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.

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.

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.

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)

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

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

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 = 0.2637

Binomial Coefficient The number of arranging k successes among n observations is given by pg 518 cant write in power point

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, Pg 518

Calculator Probability Distribution Function binompdf(n,p,X) Cumulative Binomial Probability binomcdf(n,p,X)

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

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