warm-up 6.2 binomial distribution (day 1) you pay $1 to play game a, which generates a payoff $0,...
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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
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6.1 H.W. Answers E#1(a), 2(a), 9 - 11
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6.1 H.W. Answers continued…
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Student of the day!Block 4
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Student of the day!Block 5
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Introduction to 6.2 Binomial Distribution
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Introduction to 6.2 Binomial Distribution
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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 =
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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.
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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(
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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.
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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?
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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.
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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.
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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
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