week 2 lecture gm 533

Week 2 LectureGM 533

Applied Managerial Statistics

Not to be posted or stolen, etc.

Week 2 GM 533 Lecture

• Third Graders at a local elementary school were asked their favorite ice cream of 3 choices.

• The table below summarized their choices.

Ice Cream Girls Boys

Chocolate 17 19

Vanilla 5 7

Strawberry 7 4

Week 2 GM 533 Lecture

• Before answering any questions, let’s get our totals.

Ice Cream Girls Boys Sum

Chocolate 17 19 36

Vanilla 5 7 12

Strawberry 7 4 11

Sum 29 30 59

Week 2 GM 533 Lecture

• What is the probability we randomly choose a girl?

Ice Cream Girls Boys Sum

Chocolate 17 19 36

Vanilla 5 7 12

Strawberry 7 4 11

Sum 29 30 59

29 of the total 59 students are girls so the probability is29/59 or the decimal form (0.492)

Week 2 GM 533 Lecture

• What is the probability the student is a girl given that the student prefers vanilla?

Ice Cream Girls Boys Sum

Chocolate 17 19 36

Vanilla 5 7 12

Strawberry 7 4 11

Sum 29 30 59

It was “given that” the studentprefers vanilla, so we are ONLY DEALING with the 12 students whoprefer vanilla, so the probability is5/12 or the decimal form (0.417)

Week 2 GM 533 Lecture

• What is the probability the student prefers vanilla given the student is a girl?

Ice Cream Girls Boys Sum

Chocolate 17 19 36

Vanilla 5 7 12

Strawberry 7 4 11

Sum 29 30 59

It was “given that” the studentis a girl, so we are ONLY DEALING with the 29 students whoAre girls, so the probability is5/29 or the decimal form (0.172)NOTE THE DIFFERENCE FROM THEPREVIOUS EXAMPLE

Week 2 GM 533 Lecture

• Bob is playing two games with his family. In one game he has a 30% chance of winning, in the other, he has a 80% chance of winning. What is the probability Bob will lose both games?

Week 2 GM 533 Lecture

• He would have to lose the first game AND the second game. The probability of winning was given, thus we will use the complement as the probability of losing. Remember he has to lose both (so we multiply).

(1 - 0.30)(1 - 0.80) = (0.7)(0.2) = 0.14

Week 2 GM 533 Lecture

• The probability that a component will work is 95%. If we choose three of these components at random, what is the probability they will all work?

Week 2 GM 533 Lecture

• This would be

(0.95)^3 or (0.95)(0.95)(0.95) = 0.857

• The probability that none will work would be

(0.05)^3 or (0.05)(0.05)(0.05) = 0.000125

Week 2 GM 533 Lecture

• A new product is being manufactured and it has been determined the following probability distribution holds for its profitability.

Profit Probability of Scenario

($100,000) 0.25

$50,000 0.55

$250,000 0.20

Week 2 GM 533 Lecture

• The company asks your opinion on the overall profitability. Consider the - $100K as the cost to produce the new product.

(-100000)(0.25) + (50,000)(0.55) + (250,000)(0.20) = $52,500

It seems we will realize a profit of $52,000, we might need otherparameters or guidance.

Week 2 GM 533 Lecture

• A staffing company estimates that 90% of their placements last at least 4 weeks. Looking at a random sample of 17 placements, calculate the mean number of placements that will stay at least 4 weeks.

Week 2 GM 533 Lecture

• A staffing company estimates that 90% of their placements last at least 4 weeks. Looking at a random sample of 17 placements, calculate the mean number of placements that will stay at least 4 weeks.

np = 17(0.9) = 15.3

Week 2 GM 533 Lecture

• Your product works 98% of the time when it hits the market. If you randomly call 15 of your new customers, what is the probability that at least 13 of your new customers will have had a good first experience with your new product?

Week 2 GM 533 Lecture

• I took a binomial approach (it either worked or didn’t)

0.9970

Week 2 GM 533 Lecture

• You can find the binomial template and other cool statistical templates at

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

Just download the file to your computer and go to the “Review” tab at the top of Excel and select “Unprotect Sheet” (this allows you to use your own data, etc.)

Week 2 GM 533 Lecture

• Paula’s Pizza has a 90% chance of delivering their pizzas in under 37 minutes. Out of 11 deliveries, what is the probability that fewer than 9 pizzas will be delivered within 37 minutes?

Week 2 GM 533 Lecture

• Using Binomial Template

“Fewer than 9”would be the same as“At most 8” sothe probabilitywould be0.0896

Week 2 GM 533 Lecture

• A quiz has 20 multiple choice questions with four possible answers for each question. If only one of the answers is correct and a student guesses on all questions, what is the probability that the student will get at least half of the questions correct?

Week 2 GM 533 Lecture

• Use Binomial Template

At least halfwould be at least10 of the 20questions.The answer wouldbe 0.0139Not too hot eh?

Week 2 GM 533 Lecture

• I will post a link to these charts on my Statcave site at http://www.facebook.com/statcave

• You DO NOT have to be a Facebook person to see this

• It is convenient for me to post there.