1. Binomial and Geometric Distributions Notes on your own paper

2. Binomial Distributions, B(n,p) Each trial results in one of two mutually exclusive outcomes. (success/failure) There are a fixed number of trials Outcomes of different trials are independent The probability that a trial results in success is the same for all trials The binomial random variable x is defined as the number of successes out of the fixed number

3. Refresher on Binomial Probability P(x<k) = binomialcdf(n,p,k) Where: n is the sample size, and p is the probability P(15<x<30) = Binomialcdf(n,p,30) – binomialcdf(n,p,14) For example, if n=250 and p=.1, To calculate P(x<30), we would use: P(x<30) = binomialcdf(250,.1,30)

4. Binomial Formulas (on chart) For mean and standard deviation:

5. Binomial Formulas For probability: (on chart) Combination: n,Math,PRB, n C r,k, enter (NOT on chart)

6. The number of inaccurate gauges in a group of eight is a binomial random variable. If the probability of a defect is 0.1, what is the probability that only 3 are defective? K= n= p= 3 8.1

7. Calculator: = 8, Math,PRB, n C r,3 enter = 56 8383 Then, P(x=3) = (56)(0.1) 3 (0.9) 5 =.0331 See #4b on Graded Assignment 2- 2

8. Geometric Distributions The random variable x is the number of trials UNTIL the FIRST success occurs. “When” something occurs. The difference between binomial and geometric properties is that there is NOT a fixed number of trials in geometric distributions!

9. Geometric Formulas (NOT on chart) Memorize these!

10. Calculator: 2 nd VARS P(X = k) = geometpdf(p,x) finds the geometric probability P(X < k) = geometcdf(p,x) finds the cumulative probability No “ n ” because there is no fixed number!

11. A real estate agent shows a house to prospective buyers. The probability that the house will be sold to the person is 35%. What is the probability that the agent will sell the house to the third person she shows it to? OR P(x) = p(1-p) x-1 so P(x=3) =.35(.65) 2 =.1479 See #5 on Graded Assignment 2- 2

12. Homework: Quiz tomorrow, study: Page 142 in AP Format Graded Assignment 2-2 How to interpret Quantile plot Describe a distribution (CUSS)