Week 2 Lecture for GM 533 - Applied Managerial Statistics

1. Week 2 Lecture
GM 533
Applied Managerial Statistics
Not to be posted or stolen, etc.

2. 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

3. 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

4. Week 2 GM 533 Lecture
• What is the probability we randomly choose a
girl?
Ice Cream Girls Boys Sum
29 of the total 59 students are
Chocolate 17 19 36 girls so the probability is
29/59 or the decimal form (0.492)
Vanilla 5 7 12
Strawberry 7 4 11
Sum 29 30 59

5. 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
It was “given that” the student
Chocolate 17 19 36 prefers vanilla, so we are ONLY
DEALING with the 12 students who
Vanilla 5 7 12 prefer vanilla, so the probability is
5/12 or the decimal form (0.417)
Strawberry 7 4 11
Sum 29 30 59

6. Week 2 GM 533 Lecture
• What is the probability the student prefers
vanilla given the student is a girl?
Ice Cream Girls Boys Sum
It was “given that” the student
Chocolate 17 19 36 is a girl, so we are ONLY
DEALING with the 29 students who
Vanilla 5 7 12 Are girls, so the probability is
5/29 or the decimal form (0.172)
Strawberry 7 4 11 NOTE THE DIFFERENCE FROM THE
PREVIOUS EXAMPLE
Sum 29 30 59

7. 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?

8. 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

9. 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?

10. 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

11. 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

12. 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 other
parameters or guidance.

13. 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.

14. 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

15. 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?

16. Week 2 GM 533 Lecture
• I took a binomial approach (it either worked
or didn’t)

17. 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.)

18. 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?

19. Week 2 GM 533 Lecture
• Using Binomial Template
“Fewer than 9”
would be the
same as
“At most 8” so
the probability
would be
0.0896

20. 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?

21. Week 2 GM 533 Lecture
• Use Binomial Template
At least half
would be at least
10 of the 20
questions.
The answer would
be 0.0139
Not too hot eh?

22. 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.