Warm-up6.2 Binomial Distribution (Day 1)

You pay $1 to play Game A, which generates a payoff$0, $1, $2, or $3 with respective probabilities 0.4, 0.3, 0.2,and 0.1. You also pay $2 to play Game B, which generates a payoff

$0,$2, or $4 with respective probabilities 0.7, 0.2, and 0.1. Thegames are operated independently of each other.

• Find the expected value of Game A and Game B.• Calculate your expected gain for each game. Expected Gain = Expected Value – Initial investment

6.1 H.W. Answers E#1(a), 2(a), 9 - 11

6.1 H.W. Answers continued…

Student of the day!Block 4

Student of the day!Block 5

Introduction to 6.2 Binomial Distribution

Introduction to 6.2 Binomial Distribution

6.2 Binomial Distribution (Day 1) Binomial Random Variable (k) : is the number of trials that was successful or favorable.-The range of k is all whole numbers between 0 to n, where n represents the total number of trials.

Binomial Distribution: the probability distribution of a binomial random variable from 0 to n. - Usually see symbol B(n, p).

Examples of binomial distribution:•The number of correct responses in a 30 multiple choice question test with 5 choices for each question. k = p = b. A survey of a proposition for an upcoming election where only responses are yes or no. k = p =

First problem of Binomial DistributionThe proportion of adults age 25 and older in the United Stateswith at least a bachelor’s degree is 0.27. Suppose you pickseven adults at random. What is the probability that exactlythree will have a bachelor’s degree or higher? B(n, p , x) is how the problem is written where X is the

number of successes. 0 < X < n * The book uses k, other books and the calculator directions refer to this as x.

First:

The formula:

!)(!

!

knk

nCkn

nk

knknk pp )1(

The formula gives us the probability that event occurs.

Second Binomial Distribution ProblemAccording to a recent government report,73% of driversnow use seat belts regularly. Suppose a police officer at aroad check randomly stops four cars to check for seatbeltusage. Find the probability distributionof X, the number ofdrivers using seat belts. knkn

k pp )1(

Another calculator shortcut

Binomcdf is the command used to find the proportion of successes that are at k or less (area under the curve).If you wanted to find the proportion of 2 or less out of the four people stopped were wearing seatbelts, use thisfunction.

Individual PracticeAbout 8.8% of people ages 14–24 are “dropouts,” persons who are notIn regular school and who have not completed the 12th grade orreceived a general equivalency degree. Suppose you pick five people at Random from this age group. a. Make a probability distribution table for this situation. b. What is the probability that none of the five are dropouts. c. What is the probability that at least one is a dropout?

A.P. Student Evaluation Form• I know at times some of you make suggestions and I have followed

through with your ideas.• I am aware that some of you have ideas to making this class better

, I will be glad if you share them with me on paper since I know some of you are not comfortable approaching me in person.

• Do not write your name on the Evaluation Form• Please be aware, the graduate course on Teaching Probability and

Statistics and the A.P. Statistics teacher training workshop I took was 2 or 3 years ago.

• I know some of you wonder what resources I use in addition to the textbook: 1) 5 Steps to a 5 2) A Cartoonist’s Guide to Statistics 3) Stats: Modeling the World by Bock, Velleman, and De Veaux 4) How to Lie with Statistics 5) Dr. Tang’s Statistics Notes: http://www.doctortang.com/AP%20Statistics/units.htm

• Also for ideas and suggestions on the last part, I want to hear of some ideas for what we can do when we run out of Student of the day sheets.

Finish the other side of the Cumulative Prob. Worksheet• Finish the other side of the Cumulative Prob.

Worksheet• I will collect these at the end of the block• Next block we will cover 6.2 (Day 2) and review for the

quiz by doing a Whiteboard game doing Multiple Choice Questions.

• The quiz on Thursday February 2nd is not multiple choice.

• Be sure you know how to find expected value and standard deviation for a probability distribution and a binomial distribution. You should also know how to complete or create a probability distribution table and a binomial distribution table.

Statistics Evaluation Form

• I know at times some of you make suggestions and I have followed through with your ideas.

• I am aware that some of you have ideas to making this class better , I will be glad if you share them with me on paper since I know some of you are not comfortable approaching me in person.

• Do not write your name on the Evaluation Form