This document provides examples and solutions for statistics homework problems using binomial, geometric, and Poisson distributions in Minitab software. It addresses three homework problems on finding probabilities for the number of households reporting they feel secure, the number of sales calls required, and the number of hurricanes hitting an island. Step-by-step instructions are given for setting up each problem in Minitab and calculating the requested probabilities. None of the probabilities calculated are described as unusual.

1. Week 4 Three Extra Homework
Examples (3x9)/W
MA 221
Statistics for Decision Making
Professor Brent Heard
Not to be copied or linked to
without my permission

2. (3x9)/W
• Disclaimer
▫ Please note that I might do things a little
differently than your instructor, your tutor, your
friends, your mother, your dog, etc.
▫ The reason I post these examples is to help you
▫ There is no requirement for you to even look at
these
▫ Therefore, if I help you – great. If I don’t – I’m
sorry.
▫ This is something I simply do as a service to the
students because I like them!

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• Number 5 Example
▫ On number 5 in the homework, they are just
trying to get you to use the Binomial to find the
probability of certain things happening based on a
given n and p.
▫ It’s really easy. Let’s look at an example…

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• Forty-two percent of households say they would
feel secure if they had six months of expenses in
the bank. You randomly select 9 households and
ask them if they would feel secure having six
months worth of their expenses in the bank.
▫ Find the probability exactly 6 would say yes.
▫ Find the probability more than 6 would say yes.
▫ Find the probability that at most 6 would say yes.
• Solution next page

5. (3x9)/W
• Based on our question, we know we are asking 9
households, so n=9. Also we know that 42% feel
secure having that amount saved, so p=0.42 (the
decimal form of 42%)
• The rest is easy using Minitab…
▫ I use the same approach in Minitab to solve all
three parts of this question
▫ I recently discovered that it works very well

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• Once in Minitab
▫ Go to Graph >> Probability Distribution Plot
 Once There Click the Fourth Option “View Probability”
and then Click “OK”

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• Now in Probability
Distribution Plot
▫ Now for this
problem, change the
Distribution Dropdown
to “Binomial” and input
the n (number of trials)
and p (Event
probability) for this
problem (Remember 9
households, so n=9.
Forty-two percent, so p
= 0.42

8. (3x9)/W
• Now click the Shaded Area Tab and pay attention

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• For this problem we
will be putting in “X
values
• For Exact values like
P(x=6), we will use
“Middle,” for less
than problems we
will use “Left Tail”
and for greater than
problems, we will use
“Right Tail”
• But pay attention to
the wording!

10. (3x9)/W
• Now part “a” was to find P(6) based on n=9 and p=0.42
Therefore, P(6) = 0.08996 or 0.090
rounded to three decimal places

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• Now part “b” was to find “more than 6” based on n=9 and p=0.42. “More
than 6 implies “7 or more.” This is a “Right Tail.”
Therefore, P(x>6) = 0.03338 or 0.033
rounded to three decimal places

12. (3x9)/W
• Now part “c” was to find the probability of “no more than 6” based on n=9
and p=0.42. “No more than 6” implies “6 or less.” This is a “Left Tail.”
Therefore, P(x<=6) is 0.9666 or 0.967
rounded to three decimal places

13. (3x9)/W
• These are easy, just follow the steps and
remember on those “More than 6” type
problems, you are dealing with a right tail
where “more than 6” means 7 or more…
• Steps again - Graph >> Probability
Distribution Plots
• Next page

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• Order
Pick Tails
and
values
based on
problem
See
Answer

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• Number 13 Example
▫ On number 13 in the homework, they are just
trying to get you to use the Geometric distribution
to find the probability of something happening on
the 4th time or 5th or a certain “one shot” time. In
other words, when the event happens – game over
(You’ve done it for “the first time.”)
▫ It’s really easy. Let’s look at an example…

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• Number 13 Example
▫ Assume the probability you will make a sale on
any given phone call is 0.11. Find the probability
that you
 A) make your first sale on the third call
 B) make your first sale on the
first, second, third, fourth, fifth or sixth call.
 C) Do not make the first sale on one of the first four
calls.

17. (3x9)/W
• Easy in Minitab
▫ Go to Graph >> Probability Distribution Plot
 Once There Click the Fourth Option “View Probability”
and then Click “OK”

18. (3x9)/W
• Now in Probability
Distribution Plot
▫ Now for this
problem, change the
Distribution
Dropdown to
“Geometric” and input
Event probability for
this problem
(Remember the
probability is 0.11)

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• Now click the Shaded Area Tab and pay attention

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• Now in Shaded Area Tab
after choosing
Geometric distribution
and inputting correct
Event Probability
▫ Part A) - Make your first
sale on the third call

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• Answer
• 0.08713 or 0.087
rounded to three
decimals

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• Now in Shaded Area Tab
after choosing Geometric
distribution and inputting
correct Event Probability
 Part B) - make your sale
on the
first, second, third, fourth
, fifth or sixth call. (THIS
MEANS MAKE YOUR
SALE IN ONE OF THE
FIRST SIX CALLS – SO
IT IS “LEFT TAIL” WITH
6 AS YOUR STOPPING
POINT)

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• Answer
• 0.5030 or 0.0503
rounded to three
decimals

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• Now in Shaded Area Tab
after choosing Geometric
distribution and inputting
correct Event Probability
 Part C) - Do not make a
sale on the first four calls.
(THIS MEANS MAKE
YOUR FIRST SALE ON
THE FIFTH CALL OR
LATER – SO THIS IS A
“RIGHT TAIL”
STARTING WITH 5.)

25. (3x9)/W
• Answer
• 0.6274 or 0.627
rounded to three
decimals

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• Last Question - Are any of these “Unusual?”
• “NO” – To be considered “Unusual” the
probability would have to be less than 0.05
• In other words, 0.0671, 0.124, 0.053 are not
unusual. However values like
0.047, 0.003, 0.019 are because they are less
than 0.05 or “5%.”

27. (3x9)/W
• Number 15 Example
▫ On number 15 in the homework, they are just
trying to get you to use the Poisson to find the
probability of something happening. Read about
the differences in Geometric and Poisson
problems, you should be able to spot them pretty
easy. With a Poisson, they usually give you an
average over a given timeframe.
▫ Let’s look at an example…

28. (3x9)/W
• Number 15 Example
▫ A major hurricane has really strong winds and if I
wanted to confuse you I would tell you how strong the
winds have to be, but I don’t want to confuse you.
During the last century the mean number of
hurricanes to hit Gilligan’s Island per year was about
0.52 (SCREAMS POISSON- “Over the last century the
average number of hurricanes per year”)
 Find the following
 Probability exactly one hurricane will hit Gilligan’s Island
 Probability at most one hurricane will strike Gilligan’s Island
 Probability more than one hurricane will hit Gilligan’s Island

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• Again back to Minitab (Should sound familiar)
▫ Go to Graph >> Probability Distribution Plot
 Once There Click the Fourth Option “View Probability”
and then Click “OK”

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• Now in Probability
Distribution Plot
▫ Now for this
problem, change the
Distribution
Dropdown to
“Poisson” and input
the mean for this
problem (Remember
the number of
hurricanes was 0.52)

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• Now click the Shaded Area Tab and pay attention

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• Now in Shaded Area Tab
after choosing
Geometric distribution
and inputting correct
Event Probability
▫ Part A) – Exactly one
hurricane

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• Answer
• 0.3092 or 0.309
rounded to three
decimals
• This is “NOT
UNUSUAL”
because it is
greater than 0.05

34. (3x9)/W
• Now in Shaded Area Tab
after choosing
Geometric distribution
and inputting correct
Event Probability
 Part B) – at most one
hurricane
 NOTE AT MOST ONE
IS ZERO OR ONE, SO
IT IS LEFT TAILED
WITH AN ENDPOINT
AT 1

35. (3x9)/W
• Answer
• 0.9037 or 0.904 rounded
to three decimals
▫ This is the probability of at
most one hurricane
hitting… which means it
combines the probabilities
of seeing none or zero and
one
▫ Again, this is “NOT
UNUSUAL” – as a matter
of fact there is about a
90% chance of getting
either zero or one
hurricanes

36. (3x9)/W
• Now in Shaded Area Tab
after choosing
Geometric distribution
and inputting correct
Event Probability
 Part C) – More than one
hurricane – THIS
MEANS “TWO OR
MORE” Therefore we
have a Right Tail with 2
on the left endpoint.

37. (3x9)/W
• Answer
• 0.09633 or 0.096 rounded to
three decimals – again not
unusual
• However note that if I add
my results from part b and
part c together I should get
one because I have “covered”
all possibilities (In that the
probability of seeing 1 or less
plus the probability of seeing
2 or more would be
everything
▫ (THIS IS JUST AN ATTEMPT
TO HELP YOU BETTER
UNDERSTAND
PROBABILITY
DISTRIBUTIONS)

38. (3x9)/W
• Last Question - Are any of these “Unusual?”
• “NO” – To be considered “Unusual” the
probability would have to be less than 0.05

39. (3x9)/W
• Hope you enjoyed this… Let me know if these
help!
• More examples next week….
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US