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Lecture for Week 5 QuizStatistics For Decision

Making

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Your Week 5 Quiz is on material covered in Weeks 3 and 4

Your Week 7 Quiz is on material covered in Weeks 5 and 6

Your Final Exam is comprehensive covering the material in the three prior quizzes plus the material covered in Week 7

Your best approach for preparing for the quizzes should be the Practice Questions offered in the live lecture each week we have a quiz.

Week 5 Quiz

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Week 5 Quiz

Let’s look at some questions….

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How many ways can a committee of 4 be chosen from 20 people?

Week 5 Quiz

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How many ways can a committee of 4 be chosen from 20 people?

This would be a combination because “order” doesn’t matter, so there would be 4845 different ways.

Week 5 Quiz

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How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)?

Week 5 Quiz

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How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)?

This would be a permutation because “order” does matter, so there would be 116280.

Week 5 Quiz

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What values can a probability be?

Week 5 Quiz

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What values can a probability be?

Anything between 0 and +1 (NOTHING ELSE). That also means from 0% to 100%, and any positive fraction where the numerator is smaller than the denominator.

Week 5 Quiz

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List the sample space of the National League teams in the 2008 MLB playoffs.

Week 5 Quiz

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Week 5 Quiz

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List the sample space of the National League teams in the 2008 MLB playoffs.

{Brewers, Cubs, Dodgers, Phillies}

Other Examples, Gears in my car {P, D, 2nd, Low, R, N}, Numbers on a clock {1,2,3,4,5,6,7,8,9,10,11,12}, Different weeks in our term {1,2,3,4,5,6,7,8}, Grades for the Course {A,B,C,D,F}, Standard Light Switch {On, Off}, etc.

Week 5 Quiz

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What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7? (without replacement)

Week 5 Quiz

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What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7?

What is the probability of drawing a 7 from a deck of cards? 4/52 or 1/13 And what is the probability of a second card being an Ace or King if the first was a 7? (without replacement)There are 8 Aces and Kings left, but only 51 cards to draw from so it would be 8/51

Week 5 Quiz

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What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8? (without replacement)

Week 5 Quiz

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What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8?

What is the probability of drawing a 6, 7, or 8 from a deck of cards? There would be 12 of them so 12/52 or 3/13 What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8? (without replacement)There would be 11 left and only 51 cards to draw from so it would be 11/51

If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document?

Week 5 Quiz

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If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document?

13/ (13+27) = 13/40

Week 5 Quiz

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FactorialsAnswer the following: 4! 3! * 0! 2! /0!

(0!*3!)/4!

Week 5 Quiz

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! !!

FactorialsAnswer the following: Remember that the factorial sign means x! = x * x-1 *

x-2 * … 1, so4! = 4*3*2*1 = 24 3! * 0! = (3*2*1) * 1 = 6 (remember 0! is ALWAYS = 1) 2! /0! = (2*1)/1 = 2 (remember 0! is ALWAYS = 1)

(0!*3!)/4! = (1*3*2*1)/(4*3*2*1) = 1/4 (remember 0! is ALWAYS = 1)

Week 5 Quiz

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Week 5 Quiz

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Decide whether the following experiments would be Binomials, Poissons, or neither.  1. You test 6 different types of batteries.  The random variable

represents the battery that is last longest.  Past experience is that 30% of the time it is the third of the six types.

2. You observe a stop sign for 4 hours.  The random variable represents the number of cars that either completely stopped or didn’t.  Historically 65% of cars come to a complete stop.

3.  A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup.

4.  A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective.

Week 5 Quiz

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1. You test 6 different types of batteries.  The random variable represents the battery that is last longest.  Past experience is that 30% of the time it is the third of the six types. Neither, because we are testing 6 different types (it’s not a yes/no, good/bad, two decision type situation)

2. You observe a stop sign for 4 hours.  The random variable represents the number of cars that either completely stopped or didn’t.  Historically 65% of cars come to a complete stop. Binomial, probability given in percentage. For this to be Poisson it would say something like on average 42 cars stop at the stop sign every hour, we want to know the probability of exactly 32 stopping, or more than 45 stopping, etc. – the probability (%) was a tip off that it was binomial

3.  A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup. Poisson, as per the previous question’s answer we are interested in finding out the probability of 1 pickup.

4.  A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective. Neither, we don’t have a probability to start with (Binomial), or an average number of defects (Poisson).

Week 5 Quiz

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If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable?

Week 5 Quiz

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If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable?

Yes, the sum of the probabilities = (.3+.3+.2+.2) = 1 and they are all between 0 and 1.

Find P(X < 14) for this random variable.  X = {1, 5, 7, 13, 15}.  P(1) = P(5) = P(7) = P(13) = P(15).

Week 5 Quiz

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Find P(X < 14) for this random variable.  X = {1, 5, 7, 13, 15}.  P(1) = P(5) = P(7) = P(13) = P(15).

Since  P(1) = P(5) = P(7) = P(13) = P(15) they must add up to 1 therefore the probability for each must be 1/5 since there are five so it is 0.20

then P(x < 14) = P(1) + P(5) + P(7) + P(13) = 0.20 + 0.20 + 0.20 + 0.20 = 0.80

Week 5 Quiz

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If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable?

Week 5 Quiz

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If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable?

Do the probabilities add up to one? .3 + .1 + .3 +. 3 = 1 So yes it is (also note that those probabilities have to be between 0 and 1.)

Week 5 Quiz

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We have a binomial experiment with p = .6 and n = 3.  Set up the probability distribution and compute the mean, variance, and standard deviation.

Week 5 Quiz

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Templates for Binomial and Poisson

http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html

I will post this in the chat area of the lecture

Week 5 Quiz

See Excel Spreadsheet picture that follows.

X = {0, 1, 2, 3}P(X = 0) = 0.06 P(X = 1) = .29 P(X = 2) = .43

P(X = 3) = .22E(X) = n*p = 3 * .6 = 1.8 (listed as mean in provided excel spreadsheet picture that follows) V(X) = n*p*q, q = 1 - p = 1 - .6 = .4 V(X) = 3*.6*.4 = .72 (listed as variance in provided excel spreadsheet)standard deviation = sqrt(variance) = sqrt(.72) = .85 (listed as stdev in provided excel spreadsheet picture that follows)

Week 5 Quiz

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Week 5 Quiz

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Week 5 QuizWe have a Poisson with mu = 3. Find P(X = 4), find P(X < 4), find P(X >= 4), compute the mean, variance, and standard deviation.

Week 5 QuizSee Excel Spreadsheet attached to follow on post.P(X = 4) = 0.168 (see picture of excel spreadsheet yellow block)P(X < 4) = 0.647 (see picture of excel spreadsheet green block)P(X >=4) = 0.353 (see picture of excel spreadsheet gray block)mean = variance = 3 (see picture of excel spreadsheet)standard deviation = sqrt(variance) = 1.73 (see picture of excel spreadsheet)

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Week 5 Quiz

We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X).

Week 5 Quiz

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We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X).

E(X) = sum of (x*P(X)) = 5*P(5) + 10*P(10) = 5*.6 + 10*.4 = 3.0 + 4.0 = 7.0

Week 5 Quiz

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Continuous or discrete?

1. The amount of oil in your car’s engine?2. The number of cans of coke in your

refrigerator?3. Your son’s weight?4. The number of cousins you have?5. The amount of butter in your butter dish?6. The number of classes you have taken and

received credit for?

Week 5 Quiz

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Week 5 QuizContinuous or discrete?1. The amount of oil in your car’s engine?

Continuous2. The number of cans of coke in your

refrigerator? Discrete3. Your son’s weight? Continuous4. The number of cousins you have? Discrete5. The amount of butter in your butter dish?

Continuous6. The number of classes you have taken and

received credit for? DiscreteNot to be used, posted, etc. without my expressed permission. B Heard

Week 5 Quiz

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