Deck 5: Discrete Probability Distributions

Question 1

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.
To compute the probability of receiving at least 10 e-mails on such a day, he will use what type
Of probability distribution?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Answer 1

B

Question 2

In a binomial distribution

A) the variable X is continuous.
B) the probability of event of interest  is stable from trial to trial.
C) the number of trials n must be at least 30.
D) the results of one trial are dependent on the results of the other trials.

Answer 2

B

Question 3

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the
List whose prices are expected to rise by more than 20% after 30 days.In reality, the prices of
Only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from
The list, he would use what type of probability distribution to compute the probability that all of
The chosen stocks would appreciate more than 20% after 30 days?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Answer 3

C

Question 4

What type of probability distribution will most likely be used to analyze warranty repair needs on
New cars in the following problem?
The service manager for a new automobile dealership reviewed dealership records of the past
20 sales of new cars to determine the number of warranty repairs he will be called on to
Perform in the next 90 days.Corporate reports indicate that the probability any one of their
New cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls
For warranty repair are independent of one another and is interested in predicting the number
Of warranty repairs he will be called on to perform in the next 90 days for this batch of 20
New cars sold.

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 5

If the outcomes of a variable follow a Poisson distribution, then their

A) mean equals the standard deviation.
B) median equals the standard deviation.
C) mean equals the variance.
D) median equals the variance.

Question 6

What type of probability distribution will most likely be used to analyze the number of cars with
Defective radios in the following problem?
From an inventory of 48 new cars being shipped to local dealerships, corporate reports
Indicate that 12 have defective radios installed.The sales manager of one dealership wants to
Predict the probability out of the 8 new cars it just received that, when each is tested, no
More than 2 of the cars have defective radios.

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 7

Question 8

Question 9

.

Question 10

A company has 125 personal computers.The probability that any one of them will require repair
On a given day is 0.025.To find the probability that exactly 20 of the computers will require
Repair on a given day, one will use what type of probability distribution?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 11

Which of the following about the binomial distribution is not a true statement?

A) The probability of the event of interest must be constant from trial to trial.
B) Each outcome is independent of the other.
C) Each outcome may be classified as either "event of interest" or "not event of interest."
D) The variable of interest is continuous.

Question 12

A probability distribution is an equation that

A) associates a particular probability of occurrence with each outcome.
B) measures outcomes and assigns values of X to the simple events.
C) assigns a value to the variability of the set of events.
D) assigns a value to the center of the set of events.

Question 13

The connotation "expected value" or "expected gain" from playing roulette at a casino means

A) the amount you expect to "gain" on a single play.
B) the amount you expect to "gain" in the long run over many plays.
C) the amount you need to "break even" over many plays.
D) the amount you should expect to gain if you are lucky.

Question 14

What type of probability distribution will most likely be used to analyze the number of blue
Chocolate chips per bag in the following problem?
The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.
When the production process is in control, the mean number of blue chocolate chips per bag
Is 6.0.The manager is interested in analyzing the probability that any particular bag being
Inspected has fewer than 5.0 blue chocolate chips.

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 15

A campus program evenly enrolls undergraduate and graduate students.If a random sample of 4
Students is selected from the program to be interviewed about the introduction of a new fast food
Outlet on the ground floor of the campus building, what is the probability that all 4 students
Selected are undergraduate students?

A) 0.0256
B) 0.0625
C) 0.16
D) 1.00

Question 16

What type of probability distribution will the consulting firm most likely employ to analyze the
Insurance claims in the following problem?
An insurance company has called a consulting firm to determine if the company has an
Unusually high number of false insurance claims.It is known that the industry proportion for
False claims is 3%.The consulting firm has decided to randomly and independently sample
100 of the company's insurance claims.They believe the number of these 100 that are false
Will yield the information the company desires.

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 17

The covariance

A) must be between -1 and +1.
B) must be positive.
C) can be positive or negative.
D) must be less than +1.

Question 18

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-
Pulmonary Resuscitation (CPR).In 180 days of school, about how many days can we expect that
The teacher on bus duty will likely be certified in CPR?

A) 5 days
B) 45 days
C) 65 days
D) 81 days

Question 19

Question 20

The portfolio expected return of two investments

A) will be higher when the covariance is zero.
B) will be higher when the covariance is negative.
C) will be higher when the covariance is positive.
D) does not depend on the covariance.

Question 21

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who
Has not studied for the test decides to answer all questions randomly.What type of probability
Distribution can be used to figure out his chance of getting at least 20 questions right?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 22

True or False: Another name for the mean of a probability distribution is its expected value.

Question 23

True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a binomial distribution.

Question 24

True or False: The Poisson distribution can be used to model a continuous random variable.

Question 25

The local police department must write, on average, 5 tickets a day to keep department revenues
At budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution
With a mean of 6.5 tickets per day.Interpret the value of the mean.

A) The number of tickets that is written most often is 6.5 tickets per day.
B) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
C) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
D) The mean has no interpretation since 0.5 ticket can never be written.

Question 26

True or False: The largest value that a Poisson random variable X can have is n.

Question 27

Question 28

Question 29

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab
Conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per
Week.Interpret this value.

A) Most of the weeks resulted in rat costs of $13.00.
B) The median cost for the distribution of rat costs is $13.00.
C) The expected or mean cost for all weekly rat purchases is $13.00.
D) The rat cost that occurs more often than any other is $13.00.

Question 30

A financial analyst is presented with information on the past records of 60 start-up companies
And told that in fact only 3 of them have managed to become highly successful.He selected 3
Companies from this group as the candidates for success.To analyze his ability to spot the
Companies that will eventually become highly successful, he will use what type of probability
Distribution?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 31

True or False: The number of customers arriving at a department store in a 5-minute period has a
binomial distribution.

Question 32

True or False: The number of customers arriving at a department store in a 5-minute period has a
Poisson distribution.

Question 33

True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson
process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6
planes arrive in the next minute is 0.05041.

Question 34

True or False: In a Poisson distribution, the mean and standard deviation are equal.

Question 35

True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a hypergeometric distribution.

Question 36

True or False: Suppose that a judge's decisions follow a binomial distribution and that his verdict
is incorrect 10% of the time.In his next 10 decisions, the probability that he makes fewer than 2
incorrect verdicts is 0.736.

Question 37

Question 38

True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

Question 39

On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery
Store.What type of probability distribution can be used to find out the probability that there will
Be no customer arriving at a checkout counter?

A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Question 40

True or False: In a Poisson distribution, the mean and variance are equal.

Question 41

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the expected value gain if you invest in both houses?

Question 42

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the total standard deviation of value gain if you invest in
both houses?

Question 43

True or False: The variance of the sum of two investments will be equal to the sum of the
variances of the two investments plus twice the covariance between the investments.

Question 44

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the variance of the gain in value for the house in
neighborhood A?

Question 45

True or False: The expected return of a two-asset portfolio is equal to the product of the weight
assigned to the first asset and the expected return of the first asset plus the product of the weight
assigned to the second asset and the expected return of the second asset.

Question 46

True or False: The covariance between two investments is equal to the sum of the variances of
the investments.

Question 47

True or False: The expected return of the sum of two investments will be equal to the sum of the
expected returns of the two investments plus twice the covariance between the investments.

Question 48

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 10% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?

Question 49

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the total variance of value gain if you invest in both houses?

Question 50

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 10% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?

Question 51

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest half of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?

Question 52

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the covariance of the two houses?

Question 53

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the expected value gain for the house in neighborhood A?

Question 54

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest half of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?

Question 55

True or False: The variance of the sum of two investments will be equal to the sum of the
variances of the two investments when the covariance between the investments is zero.

Question 56

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the standard deviation of the value gain for the house in
neighborhood A?

Question 57

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the variance of the gain in value for the house in
neighborhood B?

Question 58

True or False: If the covariance between two investments is zero, the variance of the sum of the
two investments will be equal to the sum of the variances of the investments.

Question 59

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the expected value gain for the house in neighborhood B?

Question 60

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, what is the standard deviation of the value gain for the house in
neighborhood B?

Question 61

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the standard deviation of your profit when Design B is
chosen?

Question 62

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, if you decide to choose Design A for half of the production lines and
Design B for the other half, what is your expected profit?

Question 63

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 30% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?

Question 64

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if your investment preference is to maximize your expected return
while exposing yourself to the minimal amount of risk, will you choose a portfolio that will
consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the
remaining on the house in neighborhood B?

Question 65

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the total variance of the profit if you increase the shift of
your production lines and choose to produce both designs?

Question 66

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the expected profit if you increase the shift of your
production lines and choose to produce both designs?

Question 67

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if your investment preference is to maximize your expected return
and not worry at all about the risk that you have to take, will you choose a portfolio that will
consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the
remaining on the house in neighborhood B?

Question 68

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is your expected profit when Design A is chosen?

Question 69

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is your expected profit when Design B is chosen?

Question 70

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the total standard deviation of the profit if you increase the
shift of your production lines and choose to produce both designs?

Question 71

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if your investment preference is to minimize the amount of risk that
you have to take and do not care at all about the expected return, will you choose a portfolio that
will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A
and the remaining on the house in neighborhood B?

Question 72

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, the table above is called the ______________ for the two designs.

Question 73

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 70% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?

Question 74

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the standard deviation of your profit when Design A is
chosen?

Question 75

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the variance of your profit when Design A is chosen?

Question 76

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 90% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?

Question 77

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 30% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?

Question 78

SCENARIO 5-2
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers
when winter arrives.The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Referring to Scenario 5-2, what is the variance of your profit when Design B is chosen?

Question 79

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 70% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?

Question 80

SCENARIO 5-1
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition.The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-1, if you can invest 90% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?