QM120_2S01
:
‫أستاذ المادة‬
: ‫رقم الشعبة أو وقتها‬
: ‫اسم الطالب‬
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__________________________
: ‫رقم الطالب‬
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Second Exam – QM 120 - Spring 2001/2002
Question (1):
A small drug store ordered copies of a news magazine for its magazine rack each week. Let X be a
random variable that represents the demand for the magazine, with the following probability mass
(density) function:
X
P(X=x)
1
1/15
2
2/15
3
3/15
4
4/15
5
3/15
6
2/15
o/w
0
(a) What is the expected demand for the magazine, its variance and its standard deviation?
(b) What is the probability that the demand exceeds 4 magazines?
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(c) What is the probability that the demand is at most 3 magazines?
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(d) What is the probability that the demand is greater than 2 and less than 5 magazine?
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(e) Form the probability cumulative distribution function?
X
<1
1
2
3
4
F(X)
5
6
>6
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QM120_2S01
Question (2):
An investor has a portfolio of stock investments in Banks (B) and in Industrial (I) shares. He has
monitored the prices of his portfolio investments for 180 days, and found:
Banks (B)
Industrial (I)
Price movement of the shares
Prices
Prices did
Prices
went up
not change went down
(U)
(F)
(D)
60
30
20
40
15
TOTAL
15
TOTAL
If a share type is chosen at random from his portifolio. Find the following:
(1) The probability that the share price of that type went up in the last six months (180 days)?
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(2) What is the probability that the price of the chosen share did not change for the industrial type
of shares in the last six months (180 days)?
(3) Are the price movement and share type Mutually Exlusive? And why?
(4) What is the probability that the chosen share is either from Bank shares or its price went down?
(5) Find the probability of the event : ( F  B )? (Show your work)
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QM120_2S01
Question (3):
To investigate the impact of promoting certain product on the company’s sales, a sales engineer
checked the company’s records for some statistical support. From the records, she found that the
company has made promotion to 40% of its product in the past. From the records she also found
that, if the company made promotion to its product before launching, there would 80% chance to
make a sale within the first month after launching the product. However, if the company did not
promote the product, there is a 90% chance of not making a sale within the first month after
launching the product. Let “A” be the event that product is promoted and “B” is the event that a
sale has been made.
Draw the probability tree, hence answer the following questions:
(1) Write down the sample space of this random experiment?
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(2) What is the probability that a sale was made?
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(3) If we know that a sale was made. What is the probability that the product was not promoted?
(4) Are sale and promotion independent events? Justify (i.e. state your reasons)?
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QM120_2S01
Question (4):
The following is the Minitab output of the numbers of computer terminals produced at certain
company for a sample of 30 days:
Raw Data:
20
21
22
23
23
23
23
24
25
26
26
27
27
27
27
28
28
28
29
29
31
31
31
32
33
33
33
34
35
35
The following is the output from MINITAB:
Descriptive Statistics: terminal
Variable
terminal
N
30
Mean
27.800
Median
27.500
TrMean
27.808
Variable
terminal
Minimum
20.000
Maximum
35.000
Q1
23.750
Q3
31.250
StDev
4.310
SE Mean
0.787
(1) Compute the inter quartile range of the number of terminals.?
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(2) Compute the value of the Lower Outer Fence of the Box Plot for the above data?
(3) The following is the Box Plot of the number of terminals. Looking at the box plot, we conclude
that the distribution of the number of terminals is:
 (a) Skewed to the left
 (c) Symmetric
 (b) Skewed to the right
 (d) None of the above
(4) Compute the percentage of the number of terminals
that lie between 2 standard deviations from the mean,
hence discuss whether the data closly follow Chebyshev’s
rule or the emparical rule?
(5) What is the probability that the number of terminals in any day lies inside the box?
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(6) What is the probability that the number of terminals in any given day exceeds the Upper Inner
Fence (UIF)?
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