1.A recent issue of Fortune Magazine reported that the following companies had the lowest sales per employee
among the Fortune 500 companies.
Sales per Employee
(In $1,000s)
42.20
42.19
41.99
40.88
22.56
Company
Seagate Technology
SSMC
Russel
Maxxam
Dibrell Brothers
a.
b.
c.
d.
Sales
Rank
285
414
480
485
470
How many elements are in the above data set?
How many variables are in the above data set?
How many observations are in the above data set?
Name the variables and indicate whether they are qualitative or quantitative.
ANS:
a. 5
b. 2
c. 5
d. Sales per employee: quantitative; Sales rank: qualitative
2.A sample of 50 TV viewers were asked, "Should TV sponsors pull their sponsorship from programs that draw
numerous viewer complaints?" Below are the results of the survey. (Y = Yes; N = No; W = Without
Opinion)
N
N
Y
W
N
a.
b.
W
Y
N
W
Y
N
N
Y
N
N
N
N
W
W
Y
Y
N
N
Y
N
N
N
Y
W
W
N
N
W
N
Y
N
Y
W
W
Y
Y
N
N
Y
N
Construct a frequency distribution and a bar graph.
Construct a relative frequency distribution and a pie chart.
ANS:
a and b
Relative
Frequency
Frequency
No
24
0.48
Yes
15
0.30
Without Opinion
11
0.22
50
1.00
Total
3.The grades of 10 students on their first management test are shown below.
94
68
a.
61
75
96
85
66
84
92
78
Construct a frequency distribution. Let the first class be 60 - 69.
N
N
Y
W
Y
b.
c.
Construct a cumulative frequency distribution.
Construct a relative frequency distribution.
ANS:
a.
b.
Cumulative
Frequency
3
5
7
10
c.
Relative
Class
Frequency
Frequency
60 - 69
3
0.3
70 - 79
2
0.2
80 - 89
2
0.2
90 - 99
3
0.3
10
1.0
Total
4.You are given the following data on the ages of employees at a company. Construct a stem-and-leaf display.
26
52
41
42
32
44
53
44
28
36
55
40
45
42
48
36
58
27
32
37
ANS:
2|6
3|2
4|0
5|2
7
2
1
3
8
6
2
5
6
2
8
7
4
4
5
8
5.The following data show the yearly salaries of football coaches at some state supported universities.
University
A
B
C
D
E
F
G
H
Salary
(in $1,000)
53
44
68
47
62
59
53
94
For the above sample, determine the following measures.
a. The mean yearly salary
b. The standard deviation
c. The mode
d. The median
e. The 70th percentile
ANS:
a. 60
b. 15.8
c. 53
d. 56
e.
62
6.The flashlight batteries produced by one of the northern manufacturers are known to have an average life of 60
hours with a standard deviation of 4 hours. Use Chebyshev’s theorem to answer the following questions.
a.
b.
c.
At least what percentage of flashlights will have a life of 54 to 66 hours?
At least what percentage of the batteries will have a life of 52 to 68 hours?
Determine an interval for the batteries' lives that will be true for at least 80% of the batteries.
(Hint: First compute the Z-score.)
ANS:
a. 56%
b. 75%
c. 60 + (2.236)(4). This indicates that at least 80% of the batteries will have lives of 51.056 to
68.944 hours.
7.A survey of a sample of business students resulted in the following information regarding the genders of the
individuals and their selected major.
Selected Major
Gender
Male
Management
40
Marketing
10
Others
30
Total
80
Female
30
20
70
120
Total
70
30
100
200
a.
b.
c.
d.
What is the probability of selecting an individual who is majoring in Marketing?
What is the probability of selecting an individual who is majoring in Management, given that
the person is female?
Given that a person is male, what is the probability that he is majoring in Management?
What is the probability of selecting a male individual?
ANS:
a. 0.15
b. 0.25
c. 0.50
d. 0.40
8.Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The
probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships
is 0.11. The probability of getting at least one of the scholarships is 0.3.
a.
b.
c.
d.
e.
What is the probability that you will receive a Merit scholarship?
Are events A and M mutually exclusive? Why or why not? Explain.
Are the two events A, and M, independent? Explain, using probabilities.
What is the probability of receiving the Athletic scholarship given that you have been awarded
the Merit scholarship?
What is the probability of receiving the Merit scholarship given that you have been awarded
the Athletic scholarship?
ANS:
a. 0.23
b. No, because P(A  M)  0
c. No, because P(A  M)  P(A) P(M)
d. 0.4783
e. 0.6111