Deck 5: Some Important Discrete Probability Distributions

Question 1

Another name for the mean of a probability distribution is its expected value.

Answer 1

True

Question 2

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

Referring to Instruction 5-4,the mean or expected value of the number of accidents is ________.

Answer 2

2.0

Question 3

Instruction 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00
Probability: 0.35 0.40 0.25
How much should the lab budget for next year's rat orders be,assuming this distribution does not change?

A)$780
B)$650
C)$520
D)$637

Answer 3

$637

Question 4

Numerical variables are classified as either discrete or continuous.

Question 5

Instruction 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.

Referring to Instruction 5-3,the mean or expected value for the number of retransmissions is ________.

Question 6

Instruction 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.

Referring to Instruction 5-3,the variance for the number of retransmissions is ________.

Question 7

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

Referring to Instruction 5-4,the probability of 3 accidents is ________.

Question 8

The variance of a discrete random variable is directly related to the standard deviation.

Question 9

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the expected value gain for the house in neighbourhood B?

Question 10

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

Referring to Instruction 5-4,the standard deviation of the number of accidents is ________.

Question 11

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the expected value gain if you invest in both houses?

Question 12

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

Referring to Instruction 5-4,the variance of the number of accidents is ________.

Question 13

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

The standard deviation of a discrete random variable is the square root of the ________.

Question 14

Instruction 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
A probability distribution is an equation that

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

Question 15

Instruction 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.

Referring to Instruction 5-3,the probability of at least one retransmission is ________.

Question 16

Instruction 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
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 expected or average cost for all weekly rat purchases is $13.00.
C)The median cost for the distribution of rat costs is $13.00.
D)The rat cost that occurs more often than any other is $13.00.

Question 17

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the expected value gain for the house in neighbourhood A?

Question 18

Instruction 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.

Referring to Instruction 5-3,the probability of no retransmissions is ________.

Question 19

Instruction 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

Referring to Instruction 5-4,the probability of at least 1 accident is ________.

Question 20

Instruction 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.

Referring to Instruction 5-3,the standard deviation of the number of retransmissions is ________.

Question 21

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the standard deviation of the value gain for the house in neighbourhood A?

Question 22

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

Question 23

The covariance between two investments is equal to the sum of the variances of the investments.

Question 24

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the total variance of value gain if you invest in both houses?

Question 25

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 30% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Question 26

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest half of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Question 27

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if your investment preference is to minimise 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 neighbourhood A and the remaining on the house in neighbourhood B?

Question 28

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest half of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

Question 29

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 30% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

Question 30

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 70% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Question 31

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the total standard deviation of value gain if you invest in both houses?

Question 32

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the standard deviation of the value gain for the house in neighbourhood B?

Question 33

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Question 34

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 70% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

Question 35

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the variance of the gain in value for the house in neighbourhood B?

Question 36

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 10% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

Question 37

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if your investment preference is to maximise 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 neighbourhood A and the remaining on the house in neighbourhood B?

Question 38

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if you can invest 10% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Question 39

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the variance of the gain in value for the house in neighbourhood A?

Question 40

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,if your investment preference is to maximise 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 neighbourhood A and the remaining on the house in neighbourhood B?

Question 41

The portfolio expected return of two investments

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

Question 42

A covariance of zero shows that two variables,X and Y are ________.

Question 43

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 44

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

Question 45

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 46

If p remains constant in a binomial distribution,an increase in n will increase the variance.

Question 47

Suppose that a judge's decisions follow a binomial distribution and that his verdict is correct 90% of the time.In his next 10 decisions,the probability that he makes fewer than 2 incorrect verdicts is 0.736.

Question 48

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 49

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 50

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

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

Question 51

The diameters of 10 randomly selected bolts have a binomial distribution.

Question 52

If p remains constant in a binomial distribution,an increase in n will not change the mean.

Question 53

A campus program evenly enrols 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)1.00
C)0.0625
D)0.16

Question 54

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

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

Question 55

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

A)The random variable of interest is continuous.
B)Each outcome is independent of the other.
C)The probability of success must be constant from trial to trial.
D)Each outcome may be classified as either "success" or "failure".

Question 56

Instruction 5-5
There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
Returns

Referring to Instruction 5-5,what is the covariance of the two houses?

Question 57

The covariance

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

Question 58

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

Which of the following statements about the covariance between two discrete random variables is true?

A)It measures the strengths of the relationship between two random variables.
B)A negative covariance indicates a negative relationship.
C)A covariance of zero indicates that the two variables are independent.
D)All of the above.

Question 60

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 61

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have five such alarms in your home and they operate independently.Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

A)Hypergeometric distribution.
B)Binomial distribution.
C)Poisson distribution.
D)None of the above.

Question 62

Instruction 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).
Referring to Instruction 5-2,the probability that all 3 businesses succeed is ________.

Question 63

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 64

Instruction 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).
Referring to Instruction 5-2,the probability that all 3 businesses fail is ________.

Question 65

Instruction 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Instruction 5-1,the probability that neither sound an alarm in the presence of smoke is ________.

Question 66

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 67

In a binomial distribution

A)the number of trials n must be at least 30.
B)the random variable X is continuous.
C)the results of one trial are dependent on the results of the other trials.
D)the probability of success p is stablefrom trial to trial.

Question 68

If n = 10 and p = 0.70,then the standard deviation of the binomial distribution is

A)14.29.
B)1.45.
C)7.00.
D)0.07.

Question 69

Whenever p = 0.1 and n is small,the binomial distribution will be

A)left-skewed.
B)right-skewed.
C)symmetric.
D)None of the above.

Question 70

What type of probability distribution will the consulting firm most likely employ to analyse 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 71

Instruction 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).
Referring to Instruction 5-2,the probability that at least 1 business succeeds is ________.

Question 72

Instruction 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).
Referring to Instruction 5-2,the probability that exactly 1 business succeeds is ________.

Question 73

Binomial distribution has ________ properties.

A)4
B)3
C)2
D)1

Question 74

If n = 10 and p = 0.70,then the mean of the binomial distribution is

A)7.00.
B)0.07.
C)14.29.
D)1.45.

Question 75

Whenever p = 0.5,the binomial distribution will

A)be right-skewed.
B)always be symmetric.
C)be left-skewed.
D)be symmetric only if n is large.

Question 76

A certain type of new business succeeds 60% of the time.Suppose that three such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).Which of the following distributions would you use to determine the probability that all of them will fail?

A)Binomial distribution.
B)Hypergeometric distribution.
C)Poisson distribution.
D)None of the above.

Question 77

Instruction 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Instruction 5-1,the probability that both sound an alarm in the presence of smoke is ________.

Question 78

Instruction 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Instruction 5-1,the probability that at least one sounds an alarm in the presence of smoke is ________.

Question 79

Instruction 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Instruction 5-1,which distribution would you use to determine the probability that all the smoke alarms will function properly in case of a fire?

Question 80

What type of probability distribution will most likely be used to analyse 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.