This document summarizes key points from a lecture on applied managerial statistics. It includes examples of calculating probabilities for binomial distributions, such as the probability of preferring a certain ice cream flavor given gender. It also discusses using the binomial distribution to calculate probabilities for a number of success events, like product placements lasting at least 4 weeks. The document recommends an Excel template for solving binomial probability problems and provides example calculations.

1. Week 2 Lecture
GM 533
Applied Managerial Statistics
Not to be posted or stolen, etc.
without my permission. Students
can download a copy for their own
personal use.

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
girls so the probability is
Chocolate 17 19 36 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
Vanilla 5 7 12 who prefer vanilla, so the
probability is 5/12
Strawberry 7 4 11 or the decimal form (0.417)
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
Vanilla 5 7 12 who are girls, so the probability is
5/29 or the decimal form (0.172)
Strawberry 7 4 11 NOTE THE DIFFERENCE
FROM THE
Sum 29 30 59 PREVIOUS EXAMPLE

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. You could 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 $52,500, 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
• This screams “Binomial”
• You can either work these in Minitab or Excel
▫ I will show you both

17. Week 2 GM 533 Lecture
• In Minitab
▫ Enter “x” in gray box
below C1 and P(x) in gray
box below C2
▫ Fill in cells under “x” with
numbers 0 through 15

18. Week 2 GM 533 Lecture
• Go to Calc >> Probability Distributions >> Binomial
• Enter 15 for number of
trials
• Enter 0.98 for Event
probability
• Select C1 (x) for Input
column and C2 (P(x)) for
Optional storage
Make sure the radial
Button is set to “Probability

19. Week 2 GM 533 Lecture
• Click OK and you
will now have see
the probabilities
under the P(x)
column
• For example, the
P(14) = 0.226093

20. Week 2 GM 533 Lecture
• For our problem,
we wanted to
know the
probability of “at
least 13” so we
will add the P(13)
+ P(14) + P(15)

21. Week 2 GM 533 Lecture
• So P(x≥13) =
0.032299 +
0.226093 +
0.738569
which is
0.996961

22. • An alternate way is to
use “Cumulative
probability” and enter
“12” for the Input
constant… This gives
you the probability of
12 or less, we could
then subtract the
result from 1 to get
the probability of 13
or more

23. Week 2 GM 533 Lecture
• 1 – 0.003094 =
0.996961
• (The same result we
got)

24. Week 2 GM 533 Lecture
• Don’t be afraid, these are easier than what you
think

25. Week 2 GM 533 Lecture
• On these type problems, I actually use an Excel
template that I will be happy to share with you

26. 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/exc
el_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.)

27. Week 2 GM 533 Lecture
• On the following problems, I am going to use the
Excel Template
• It is a matter of preference for me
• You will need to ask your instructor

28. 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?

29. 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

30. 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?

31. 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?

32. 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.