Business Statistics Test 2
1. A university recently surveyed 500 students to determine which new fitness area to offer in its recreation
facility. The results of the survey are summarized in the following table.
What is the probability that a randomly selected student prefers a climbing wall or is in Year 3-4?: 0.654; This
probability can be found using the addition rule because we want to know the probability of either thing happening. We u
the general rule, however, as the categories are not mutually exclusive. There are (81
+ 78 + 49)/500 = 208/500 students interested in a climbing wall, while there are (75 + 78 + 44)/500 = 197/500 students
who are in Year 3-4. Additionally, there are 78/500 students who are in both categories. Therefore, P(climbing wall or
Year 3-4)
= 208/500 + 197/500 78/500 = 327/500 = 0.654.
2. Each salesperson in a large department store chain is rated on their sales ability and their potential for
advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random has above-av- erage sales ability and has excellent
potential for advancement?: 0.27; The events are not independent. P(above-average ability and excellent potential) =
P(above-average ability) × P(excellent potential | above-average ability) = (300/500) (135/300) = 135/500 = 0.27.
3. An electronics firm sells four models of stereo receivers, three amplifiers, and six speaker brands. When the
four types of components are sold together, they form a "system." How many different systems can the electronics
firm offer?: 72; Using the multiplication formula, (4)(3)(6) = 72.
4. A board of directors consists of ten men and four women. A four-member search committee is randomly
chosen to recommend a new company presi- dent. What is the probability that all four members of the search
committee will be women?: 1/1001, or 0.001; There are four women in a group of 14 individuals. Therefore, the
probability of picking a woman on the first selection is 4/14, the second selection is 3/13, the third selection is 2/12, and
the fourth is 1/11. This is an application of the multiplication rule for events that are not independent. The joint
probability is (4/14)(3/13)(2/12)(1/11) = 0.001.
5. When are two experimental outcomes mutually exclusive?: If one outcome occurs, then the other cannot.
6. A study of interior designers' opinions with respect to the most desirable primary color for executive offices
showed the following:
What is the probability that a designer does not prefer blue?: 0.8575; Using the
, Business Statistics Test 2
complement rule, P(blue) = 57/400 = 0.1425. Therefore, P(not blue) = 1.00 0.1425
= 0.8575.
7. What does the complement rule state?: P(A) = 1 P(not A)
8. An Airbnb home has installed a combination lock with pushbuttons labeled A though F (six buttons) and uses
four of these buttons in any order. Pushbut- tons cannot be used more than once to unlock the door. For example,
a code such as AFDC is allowed, but AFDA is not. How many different codes does this lock provide?: 360; Using
the permutation formula, 6 P4 = 360.
9. An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some
packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are satisfactory?: -
0.729; Apply the multiplication rule: (0.90)(0.90)(0.90) = 0.729.
10.A university recently surveyed 500 students to determine which new fitness area to offer in its
recreation facility. The results of the survey are summarized in the following table:
What is the probability that a randomly selected student is interested in a spinning room given that they
are a graduate student?: 0.558; This is a
conditional probability because we are only interested in graduate students who want a spinning room. There are 87
graduate students who want a spinning room, out of (87 + 49 + 20) = 156 total graduate students, or P(spinning room|
graduate) = 87/156 = 0.558.
11.A study of 200 computer service firms revealed these incomes after taxes:
What is the probability that a particular firm selected has $1 million or more in income after taxes?: 0.46; A
couple of approaches can be used to answer the question. Using the complement rule, the probability of firms less than
$1 million is
108/200 = 0.54. The complement or firms with $1 million or more income is 1.0 0.5
= 0.46.
12.A board of directors consists of eight men and four women. A four-member search committee is randomly
chosen to recommend a new company presi- dent. What is the probability that all four members of the search
committee will be women?: 1/495, or 0.002; There are four women in a group of 12 individuals. Therefore, the
probability of picking a woman on the first selection is 4/12, the second selection is 3/11, the third selection is 2/10, and
the fourth is 1/9. This is
an application of the multiplication rule for events that are not independent. The joint probability is (4/12)(3/11)(2/10)(1/9
= 0.002.
1. A university recently surveyed 500 students to determine which new fitness area to offer in its recreation
facility. The results of the survey are summarized in the following table.
What is the probability that a randomly selected student prefers a climbing wall or is in Year 3-4?: 0.654; This
probability can be found using the addition rule because we want to know the probability of either thing happening. We u
the general rule, however, as the categories are not mutually exclusive. There are (81
+ 78 + 49)/500 = 208/500 students interested in a climbing wall, while there are (75 + 78 + 44)/500 = 197/500 students
who are in Year 3-4. Additionally, there are 78/500 students who are in both categories. Therefore, P(climbing wall or
Year 3-4)
= 208/500 + 197/500 78/500 = 327/500 = 0.654.
2. Each salesperson in a large department store chain is rated on their sales ability and their potential for
advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random has above-av- erage sales ability and has excellent
potential for advancement?: 0.27; The events are not independent. P(above-average ability and excellent potential) =
P(above-average ability) × P(excellent potential | above-average ability) = (300/500) (135/300) = 135/500 = 0.27.
3. An electronics firm sells four models of stereo receivers, three amplifiers, and six speaker brands. When the
four types of components are sold together, they form a "system." How many different systems can the electronics
firm offer?: 72; Using the multiplication formula, (4)(3)(6) = 72.
4. A board of directors consists of ten men and four women. A four-member search committee is randomly
chosen to recommend a new company presi- dent. What is the probability that all four members of the search
committee will be women?: 1/1001, or 0.001; There are four women in a group of 14 individuals. Therefore, the
probability of picking a woman on the first selection is 4/14, the second selection is 3/13, the third selection is 2/12, and
the fourth is 1/11. This is an application of the multiplication rule for events that are not independent. The joint
probability is (4/14)(3/13)(2/12)(1/11) = 0.001.
5. When are two experimental outcomes mutually exclusive?: If one outcome occurs, then the other cannot.
6. A study of interior designers' opinions with respect to the most desirable primary color for executive offices
showed the following:
What is the probability that a designer does not prefer blue?: 0.8575; Using the
, Business Statistics Test 2
complement rule, P(blue) = 57/400 = 0.1425. Therefore, P(not blue) = 1.00 0.1425
= 0.8575.
7. What does the complement rule state?: P(A) = 1 P(not A)
8. An Airbnb home has installed a combination lock with pushbuttons labeled A though F (six buttons) and uses
four of these buttons in any order. Pushbut- tons cannot be used more than once to unlock the door. For example,
a code such as AFDC is allowed, but AFDA is not. How many different codes does this lock provide?: 360; Using
the permutation formula, 6 P4 = 360.
9. An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some
packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are satisfactory?: -
0.729; Apply the multiplication rule: (0.90)(0.90)(0.90) = 0.729.
10.A university recently surveyed 500 students to determine which new fitness area to offer in its
recreation facility. The results of the survey are summarized in the following table:
What is the probability that a randomly selected student is interested in a spinning room given that they
are a graduate student?: 0.558; This is a
conditional probability because we are only interested in graduate students who want a spinning room. There are 87
graduate students who want a spinning room, out of (87 + 49 + 20) = 156 total graduate students, or P(spinning room|
graduate) = 87/156 = 0.558.
11.A study of 200 computer service firms revealed these incomes after taxes:
What is the probability that a particular firm selected has $1 million or more in income after taxes?: 0.46; A
couple of approaches can be used to answer the question. Using the complement rule, the probability of firms less than
$1 million is
108/200 = 0.54. The complement or firms with $1 million or more income is 1.0 0.5
= 0.46.
12.A board of directors consists of eight men and four women. A four-member search committee is randomly
chosen to recommend a new company presi- dent. What is the probability that all four members of the search
committee will be women?: 1/495, or 0.002; There are four women in a group of 12 individuals. Therefore, the
probability of picking a woman on the first selection is 4/12, the second selection is 3/11, the third selection is 2/10, and
the fourth is 1/9. This is
an application of the multiplication rule for events that are not independent. The joint probability is (4/12)(3/11)(2/10)(1/9
= 0.002.
