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:
‫أستاذ المادة‬
: ‫اسم الطالب‬
____________________________________________________
____________________________
: ‫رقم الشعبة أو وقتها‬
: ‫رقم الطالب‬
____________________________________________________
____________________________
_____________________________________________________________________________________________________________________
_____________
Second Exam – QM 120 - Fall 2000/2001
Question One:
To test the average length of life measured in hours for grade A battery, the manufacturer selected 25
batteries at random, the data are given below
50, 38, 56, 48, 41, 50, 51, 52, 60, 46, 41, 53, 65, 42, 37, 50, 45, 52, 56, 51, 52, 43, 38, 33, 50.
Use Minitab Output to answer the following questions
MTB > describe c1
Variable N
C1
25
Mean
48.00
Variable
C1
Minimum
33.00
Median
50.00
TrMean
47.91
Maximum
65.00
StDev
7.60
Q1
41.50
SE Mean
1.52
Q3
52.00
MTB > sort c1 c2
MTB > print c2
33
50
37
50
38
51
38
51
41
52
41
52
42
52
43
53
45
56
46
56
48
60
50
65
50
MTB > let k1=mean (c1)-2*stdev(c1)
MTB > let k2=mean(c1)+2*stdev(c1)
MTB > print k1 k2
Data Display
K1
K2
32.8013
63.1987
1. Compute the variance of the length of life of grade A battery, and its standard deviation.
2. Compute the interquartile range of the length of life of grade A battery.
3. Compute the range of the length of life of grade A battery.
4. Calculate the coefficient of variation of the length of life of grade A battery.
5. Write down hinges and fences on the following box-plot
Lower hinge =
LIF
=
LOF
=
Upper hinge =
UIF
=
UOF
=
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6. From the box-plot the distribution of the data set is skewed to
________________________________
7. Complete the following sentences from the terms: [any skewness, median, outliers, first quartile]
The box plot does not indicate presence of _____________________________
8. What is the proportion of data set which lie within 2 standard deviation far from the mean?
Boxplot
--------------------------------I
+
I-------------------------------------------+---------+---------+---------+---------+---------+C1
36.0
42.0
48.0
54.0
60.0
66.0
9. Is your answer in question 9, closer to
 chebyshev’s s rule
or to
 the empirical rule?
Question Two:
In order to promote its product a manufacturing company sends its sales engineers to clients to
advertise the product. Two sales engineers A and B will visit two different clients. The probability
that the first engineer will make a sale (event A) is 80% , while the second engineer has 70% chance to
make a sale (event B). It is also know that P( A  B)  40% .
1. Draw Venn diagram
2. What is the probability that only the first engineer will make a sale?
3. What is the probability that exactly one engineer will make a sale?
4. What is the probability that neither one of the two will make a sale?
5. What is the probability that at most one engineer will make a sale?
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6. At a given day, if the first engineer made a sale what is the probability that the second engineer
will make a sale too?
7. Given that the second engineer couldn’t make a sale, what is the probability the first engineer will
make a sale?
8. Do you think the two engineers are independent in promoting the product?
Question Three:
The following table gives a two-way classification of 500 workers selected from a large city:
COVERED by health
insurance ( C )
NOT COVERED by
health insurance (
C)
(M)
250
80
WOMEN ( M )
105
65
MEN
I) If one worker is selected at random from this group, find the probability that this worker is:
a) covered by health insurance :
b) a Men:
c) a woman given she is covered by health insurance :
d) covered by health insurance and is a woman :
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e) not covered by health insurance or is a man :
II) Are the events “man” and “covered by health insurance” mutually exclusive? Why?
III) Are the events “covered by health insurance” and “woman” independent? Why?
Question Four:
A computer company buys 75% of all compute chips from company “A” and 25% from company
“B”. It is known that 1% of all the computer chips received from company “A” are defective, and
2% of all the computer chips received from company “B” are defective. Draw the probability Tree .
One computer is found to contain a defective chips. What is the probability that this chip came
from company “A”.
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