:‫أستاذ المادة‬
______________________________________ :‫رقم الشعبة أو وقتها‬
:‫أسم الطالب‬
__________________________________________________________:‫رقم الطالب‬
_________________________________________________
__________________________________________________________
Second Exam – QM 120 – Fall 2002-2003
Question 1:
A consumer reports article on peanut butter reported the following scores for two brands:
Creamy (A) and Crunchy (B). Use the Minitab output results to answer the following questions:
Brand A
22
50
30
50
30
53
36
56
39
56
40
56
40
62
41
65
44
68
45
Brand B
34
53
34
56
36
62
40
62
42
62
42
75
47
75
47
80
50
52
Descriptive Statistics: A, B
Variable
A
B
N
19
18
Mean
46.47
52.72
Median
45.00
51.00
TrMean
46.65
52.19
Variable
A
B
Minimum
22.00
34.00
Maximum
68.00
80.00
Q1
39.00
41.50
Q3
56.00
62.00
StDev
12.51
14.25
SE Mean
2.87
3.36
1. Complete the following table, hence answer the following questions
Measure
A
B
Range
Inter Quartile Range
Coefficient of variation
Variance
Lower Inner fence
Upper Outer fence
( X  2S , X  2S )
2. Is there any mild outliers in brand B? (Show your work)
(Page: 1 )
3. Which of the two samples is more spread: A or B ?
4. Whish sample has smaller relative dispersion: A or B?
5. Which sample has better IQR? A or B?
6. For each sample compute the % of data lying between ( X  2S , X  2S )
7. Based on your results in part (6) above check one of the following: (circle the right answer)
I. The distribution of sample A is closer to: (a) Empirical rule
(b) Chebyshev’s rule
II. The distribution of sample B is closer to: (a) Empirical rule
(b) Chebyshev’s rule
Question 2:
A family that owns two cars: new car (event N) and old car (event O). For both the old car and
the new car we noted whether the car was manufactured in America (event A), Europe (event B),
or Asia (event C). Answer the following :
1. List all possible outcomes of this experiment?
2.Which outcomes are contained in the event that one car is American and the other is Asian?
3. Which outcomes are contained in the event that at least one of the two cars is not American?
4 . What is the complement of the event in (3) above?
Question 3: (part I)
A construction company is working in on two different projects. Let A be the event that the first
project is completed on time and let B similarly be for the second project. If
P( A  B)  0.9, P( A  B)  0.5, and P( A)  0.8 . Complete the probabilities on the following
Venn diagram and hence answer the questions after:
(Page: 2 )
1. What is the probability that only one project is completed on time?
2. What is the probability that no more than one project is completed on time?
3. What is the probability that at most one projects is completed on time?
4. What is the probability that at least one project is completed on time?
5. If we know that the first project will not be completed on time, what is the probability that the
second project will be completed on time?
Question 3: (Part II)
A sales engineer visits a company abroad to promote certain product. He can travel either in
winter (event W) or in summer (event S). If he travels in winter, the probability that he will
make a sale (event A) is 0.75, while if he travels in summer the probability that he will make a
sale is 0.80 . From past experience it is known that there is a 60% chance that he will travel in
winter and 40% chance to travel in summer.
1. Complete the probability tree: (write dawn the probabilities of the events in the tree)
P(A/W)
P(A/W)
P(A/S)
P(A/S)
2. What are all possible outcomes of this experiment?
(Page: 3 )
3. What is the probability that he will make a sale in his winter trip?
4. What is the probability that he will make a sale?
5. If we know that he had made a sale. What is the probability that it was in summer time?
Question 4:
Price index (as %) was determined for 50 products as shown in the following frequency table:
Classes
Freq.
MidUpper
Cumulative
(as %)
f
point (x)
boundary
Freq.
15 10
< 35
35 25
< 55
55 - 75
15
< 75
Total
50
Find the following:
1. The standard deviation of the price index?
2. The Inter-quartile range of the price index (if it is known that Q1 equals 18.33) ?
(Page: 4 )