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Due:
Wednesday, October 17, 2007 11:59 PM EDT
Current Score:
30 out of 30
Question Score
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Description
Homework 6 covers
random variables,
probability
distributions,
expected value, and
standard deviation.
Instructions
Homework 6
You are allowed four
submissions.
Due date is 11:59 pm
Monday October 15.
1.
2.5/2.5 points
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You are planning to take to a trip to Montreal, Canada during the month of April
and you want to bring clothing that is appropriate for the weather. The daily high
temperature X in degrees Celsius in Montreal during April has an average
(expected value) of 10
o
C with a standard deviation of 4
o
C. You want to convert
these Celsius temperatures to
o
F (degrees Fahrenheit). The conversion of X
into degrees Fahrenheit is Y = (9/5)X + 32.
a.
What is the expected daily high in Montreal during April in degrees
Fahrenheit?50
50
b.
What is the standard deviation of the daily high temperature in Montreal
during April in degrees Fahrenheit?7.2
7.2
2.
4.5/4.5 points
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View Full Document In a process for manufacturing glassware, glass stems are sealed by heating
them in a flame. The temperature of the flame varies a bit. Here is the
distribution of the temperature X measured in degrees Celsius:
Temperature X
540
o
545
o
550
o
555
o
560
o
Probability
0.1
0.25
0.3
0.25
0.1
a.
Find the expected value of the temperature X.550
550
b.
Find the standard deviation of the temperature X.5.701
5.701
(Use 3
decimal places.)
The target temperature is 550
o
C.
c.
What is the expected value of the number of degrees off target, X550?0
0
d.
What is the standard deviation of the number of degrees off target, X550?
5.701
5.701
3.
7/7 points
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"Digital Analysis" is an important new tool auditors use when looking for fraud.
Faked numbers in payment records, invoices, expense account claims, and
many other settings often display patterns that are NOT present in legitimate
records.
Some patterns, like too many round numbers, are obvious and easily avoided
by a clever crook. Others are more subtle. It is a surprising fact that the first digit
X of numbers in legitimate records are NOT equally distributed between 1 and
9, but follow a distribution known as
Benford's Law
. The distribution of the first
digit according to Benford's Law is shown in the first table below.
Benford's Law
First Digit X 1
2
3
4
5
6
7
8
9
Probability
.301 .176 .125 .097 .079 .067 .058 .051 .046
If first digits in a set of records appeared "at random," the nine possible digits 1
to 9 all have the same probability, that is, each of the digits 1, 2, . . . , 9 is
equally likely to be the first digit. The probability distribution of the first digit Y
according to the random model is shown in the table below.
Random Model
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This note was uploaded on 03/22/2008 for the course BUS 350 taught by Professor Reiland during the Spring '08 term at N.C. State.
 Spring '08
 reiland
 Business, Options

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