Chapter 5
Technology
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Example T.1: Using a TI-83/84 Plus Calculator to
Calculate a Poisson Probability
A popular accounting office takes in an average of 2.78
new tax returns per day during tax season. What is the
probability that on a given day during tax season the
firm will take in 4 new tax returns? Assume that the
number of tax returns follows a Poisson distribution.
Use a TI-83/84 Plus calculator to calculate this value.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.1: Using a TI-83/84 Plus Calculator to
Calculate a Poisson Probability (cont.)
Solution
We need the value of the Poisson probability for
λ = 2.78 and x = 4. Since we want the probability of
exactly four successes, we will use option
C:poissonpdf(. Press
and then
to access
the DISTR menu and then scroll down to option C.
Enter 2.78 for μ and 4 for x, as shown in the
screenshot. Thus, P  X  4   0.1544.
HAWKES LEARNING SYSTEMS
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Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.1: Using a TI-83/84 Plus Calculator to
Calculate a Poisson Probability (cont.)
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.2: Using Microsoft Excel to Calculate a
Binomial Probability
What is the probability of getting exactly six heads in
ten tosses of a fair coin?
Solution
If we define “getting a head” as a success, then we
want the probability of 6 successes. There are 10 trials
and the probability of getting a success on any trial is
0.5. Since we want the probability of exactly 6
successes, we do not want the cumulative probability,
so we will let cumulative be FALSE. So we would type
in the following formula: = BINOM.DIST(6, 10, 0.5,
FALSE).
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.2: Using Microsoft Excel to Calculate a
Binomial Probability (cont.)
This formula returns the value 0.205078125. Thus, the
probability of getting exactly six heads in ten tosses of a
fair coin is approximately 0.2051.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.3: Using Microsoft Excel to Calculate a
Poisson Probability
Suppose that a length of copper wiring averages one
defect every 200 feet. What is the probability that a
300-foot stretch will have no defects?
Solution
Each defect in the wire is independent of any other
defect, and the average number of defects in a given
length of wire is constant. Thus, this scenario can be
modeled by a Poisson distribution. Because we are
looking for the probability of seeing no defects, x = 0.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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Example T.3: Using Microsoft Excel to Calculate a
Poisson Probability (cont.)
If there is 1 defect on average every 200 feet, then we
can expect 1.5 defects for a 300-foot stretch; thus λ =
1.5. Since we want the probability of exactly 0 defects,
we do not want the cumulative probability, so we will
let cumulative be FALSE. Thus, we would enter the
following formula: = POISSON.DIST(0, 1.5, FALSE).
This formula returns the value 0.22313016. Thus, the
probability that a 300-foot section of wiring will have
no defects is approximately 0.2231.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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Example T.4: Using Microsoft Excel to Calculate
a Hypergeometric Probability
At the local grocery there are twenty boxes of cereal on
one shelf, half of which contain a prize. Suppose that
you buy three boxes of cereal. What is the probability
that all three boxes contain a prize?
Solution
Each box purchased is considered a trial, so the number
of trials is 3. A box with a prize is considered a success,
and since we are looking for the probability that all 3
trials are successes, the number of successes obtained
is also 3.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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Systems/Quant Systems, Inc.
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Example T.4: Using Microsoft Excel to Calculate
a Hypergeometric Probability (cont.)
The population size is 20. Half of the boxes in the
population are successes, so there are 10 successes in
the population. Since we want the probability of exactly
3 successes, we do not want the cumulative probability,
so we will let cumulative be FALSE. Thus, we enter the
following formula: = HYPGEOM.DIST(3, 3, 10, 20,
FALSE).
This formula returns the value 0.105263158. Thus, the
probability that all three boxes contain a prize is
approximately 0.1053.
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Example T.5: Using MINITAB to Calculate a
Cumulative Binomial Probability
A local pizza place offers free large pizzas on Thursday
nights. The offer is good provided that the customer
correctly guesses the outcome of a coin toss when the
pizza is ordered. Also, the offer can be used to receive a
maximum of four free pizzas per customer. John arrives
at the restaurant wanting to purchase at least three
pizzas. What is the probability that he will be able to
get at least three pizzas for free? Use Minitab to
calculate the probability.
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Example T.5: Using MINITAB to Calculate a
Cumulative Binomial Probability (cont.)
Solution
First, state the problem: we want to know the
probability of at least 3 successful coin flips, where
each trial (coin flip) has a 0.5 probability of success. The
number of trials is 4 since the offer can be used for a
maximum of 4 free pizzas per customer. This is the
complement of the cumulative probability of 2 or fewer
successes in 4 trials. Choose Calc ► Probability
Distributions ► Binomial. Enter 4 for the number of
trials and 0.5 for the event probability. Select Input
constant and enter 2 in the box.
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Example T.5: Using MINITAB to Calculate a
Cumulative Binomial Probability (cont.)
Make sure Cumulative probability is selected and click
OK. The Binomial Distribution dialog box is shown in
the following screenshot.
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Example T.5: Using MINITAB to Calculate a
Cumulative Binomial Probability (cont.)
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
Example T.5: Using MINITAB to Calculate a
Cumulative Binomial Probability (cont.)
The probability, 0.6875, is displayed in the Session
window. Since this is the probability of two or fewer
successful coin flips, 1 - 0.6875 = 0.3125 is the
probability of getting at least three pizzas for free.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.