Question 1
A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 10 days for this installation and check to take place. Let A be the event? “it will be more than 6 days before the machinery becomes? available” and B be the event? “it will be less than 8 days before the machinery becomes? available.” Complete parts a through g below.
a. Describe the event that is the complement of A. Choose the correct answer below.
A.
It will be less than 6 days before the machinery becomes available.
B.
It will be no more than 6 days before the machinery becomes available.
C.
It will be less than 8 days before the machinery becomes available.
D.
It will be 6 days before the machinery becomes available.
b. Describe the event that is the intersection of events A and B. Choose the correct answer below.
A.
It will be less than 6 days or more than 8 days before the machinery becomes available.
B.
It will be less than 6 days and more than 8 days before the machinery becomes available.
C.
It will be more than 6 days or less than 8 days before the machinery becomes available.
D.
It will be more than 6 days and less than 8 days before the machinery becomes available.
c. Describe the event that is the union of events A and B. Choose the correct answer below.
A.
It will be less than 6 days or more than 8 days before the machinery becomes available.
B.
It will be more than 6 days and less than 8 days before the machinery becomes available.
C.
It will be more than 6 days or less than 8 days before the machinery becomes available.
D.
It will be less than 6 days and more than 8 days before the machinery becomes available.
d. Are events A and B mutually? exclusive?
A.
?Yes, because there are no basic outcomes present in both events.
B.
?Yes, because the basic outcome that the machinery takes exactly 7 days to become available is a basic outcome in both events.
C.
?No, because there are no basic outcomes present in both events.
D.
?No, because the basic outcome that the machinery takes exactly 7 days to become available is a basic outcome in both events.
e. Are events A and B collectively? exhaustive?
A.
?Yes, because the basic outcome that the machinery takes exactly 11 days to become available is not present in either event.
B.
?No, because the basic outcome that the machinery takes exactly 11 days to become available is not present in either event.
C.
?No, because every possible number of days from 0 to 10 that the machinery could take to become available is either more than 6 days or less than 8 days.
D.
?Yes, because every possible number of days from 0 to 10 that the machinery could take to become available is either more than 6 days or less than 8 days.
f. The event left parenthesis Upper A intersect Upper B right parenthesis union left parenthesis Upper A overbar intersect Upper B right parenthesis is equivalent to what? event?
A.
Upper A union Upper B
B.
B
C.
A
D.
Upper A union Upper A overbar
g. The event Upper A union left parenthesis Upper A overbar intersect Upper B right parenthesis is equivalent to what? event?
A.
B
B.
Upper A union Upper B
Your answer is correct.C.
Upper A union Upper A overbar
D.A
Question 2 .
A manager has available a pool of 9 employees who could be assigned to a? project-monitoring task. 4 of the employees are women and 5 are men. 3 of the men are brothers. The manager is to make the assignment at random so that each of the 9 employees is equally likely to be chosen. Let A be the event? “chosen employee is a? man” and B the event? “chosen employee is one of the? brothers.”
a. Find the probability of A.
b. Find the probability of B.
c. Find the probability of the intersection of A and B.
Questions 3
A financial analyst was asked to evaluate earnings prospects for ten corporations over the next year and to rank them in order of predicted earnings growth rates.
a. How many different rankings are? possible?
b. ?If, in? fact, a specific ordering is the result of a? guess, what is the probability that this guess will turn out to be? correct?
Questions 4
Shown below is a contingency table of probabilities for television viewing and income. What is the conditional probability of ?”Middle Income?,” given ?”Regular??”
VIEWING FREQUENCY HIGH INCOME MIDDLE INCOME LOW INCOME TOTALS
Regular 0.050.05 0.150.15 0.100.10 0.300.30
Occasional 0.100.10 0.350.35 0.050.05 0.500.50
Never 0.050.05 0.100.10 0.050.05 0.200.20
Totals 0.200.20 0.600.60 0.200.20 1.00
The conditional probability of ?”Middle Income?,” given ?”Regular?,” is
Question 5
A survey carried out for a supermarket classified customers according to whether their visits to the store are frequent or infrequent and whether they? often, sometimes, or never purchase generic products. The accompanying table gives the proportions of people surveyed in each of the six joint classifications. Complete parts? (a) through? (h).
Frequency
of Visit
OftenOften SometimesSometimes NeverNever
FrequentFrequent 0.210.21 0.450.45 0.120.12
InfrequentInfrequent 0.060.06 0.090.09 0.07
a. What is the probability that a customer is both a frequent shopper and often purchases generic? products?
b. What is the probability that a customer who never buys generic products visits the store infrequently??
c. Are the events ?”Never buys generic? products” and? “Visits the store infrequently?” ?independent?
d. What is the probability that a customer who frequently visits the store sometimes buys generic? products?
e. Are the events ?”Sometimes buys generic? products” and? “Visits the store frequently?” ?independent?
f. What is the probability that a customer infrequently visits the? store?
g. What is the probability that a customer never buys generic? products?
h. What is the probability that a customer either infrequently visits the store or never buys generic products or? both?
Question 6
For the? following, indicate if a discrete or a continuous random variable provides the best definition.
The number of home theater systems sold per month at an electronics store
Choose the correct answer below.
Discrete
Continuous
Question 7
Consider the probability distribution function below.
x 0 1
Probability 0.450.45 0.55
a. Draw the probability distribution function.
b. Calculate and draw the cumulative probability function.
c. Find the? mean, mu Subscript Upper X?, of the random variable X.
d. Find the? variance, sigma Subscript Upper X Superscript 2?, of X.
a. Choose the correct graph below.
b. Calculate the cumulative probability function Upper F left parenthesis x 0 right parenthesis.
c. mu Subscript Upper Xequals
d. sigma Subscript Upper X Superscript 2equals
Question 8
For a binomial probability function with Pequals0.5 and nequals13?, find the probability that the number of successes is equal to 8 and the probability that the number of successes is fewer than 7.
P(8 ?successes)
P(fewer than 7 ?successes)
Question 9
Assume that the number of network errors experienced in a day on a local area network? (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.2 . What is the probability that in any given day less than three network errors will? occur?
Question 10
The accompanying table? shows, for? credit-card holders with one to three? cards, the joint probabilities for the number of cards owned? (X) and number of credit purchases made in a week? (Y). Complete parts a through c below.
Number of Cards? (X)
Number of Purchases in Week? (Y)
0 1 2 3
4
1
0.080.08 0.120.12 0.090.09 0.060.06 0.040.04
2
0.030.03 0.080.08 0.070.07 0.080.08 0.080.08
3
0.010.01 0.040.04 0.050.05 0.070.07 0.10
a. For a randomly chosen person from this? group, what is the probability distribution for the number of purchases made in a? week?
Number of Cards? (X)
Number of Purchases in Week? (Y)
0 1 2 3 4
X
For a person in this group who has three? cards, what is the probability distribution for number of purchases made in a? week?
Number of Cards? (X)
Number of Purchases in Week? (Y)
0 1 2 3 4
3
c. Are the number of cards owned and number of purchases made statistically? independent?
A.
?Yes, because the joint probabilities are the products of the marginal probabilities. Statistical independence means? that, for all pairs of values x and? y, Upper P left parenthesis x comma y right parenthesis equals Upper P left parenthesis x right parenthesis Upper P left parenthesis y right parenthesis.
B.
?No, because the joint probabilities are not the products of the marginal probabilities. Statistical independence means? that, for all pairs of values x and? y, Upper P left parenthesis x comma y right parenthesis equals Upper P left parenthesis x right parenthesis Upper P left parenthesis y right parenthesis.
.C.
?Yes, because the joint probabilities are not the products of the marginal probabilities. Statistical independence means? that, for all pairs of values x and? y, Upper P left parenthesis x comma y right parenthesis not equals Upper P left parenthesis x right parenthesis Upper P left parenthesis y right parenthesis.
D.
?No, because the joint probabilities are the products of the marginal probabilities. Statistical independence means? that, for all pairs of values x and? y, Upper P left parenthesis x comma y right parenthesis not equals Upper P left parenthesis x right parenthesis Upper P left parenthesis y right parenthesis.
