Deck 3: Probability Concepts and Distributions

Question 1

What is the probability of choosing a day of the week that begins with T (Tuesday or Thursday)?

A)
B)
C)
D)

Answer 1

Question 2

Which of the following is true of classical probability?

A)It is based on theoretical arguments.
B)It is determined by historical data and past outcomes.
C)It is based on experimental data.
D)It is based on personal judgment.

Answer 2

It is based on theoretical arguments.

Question 3

There are seven applicants for a job in the 20-29 age group,fourteen in their thirties,and four in the 40-49 age group.What is the probability that the person hired will be older than 29?

A)
B)
C)
D)

Answer 3

Question 4

The probability of the complement of an event W is ________.

A)the probability of all of the outcomes that are not in that event W
B)twice the probability of the original event W
C)usually the same as the probability of event W
D)the square of the probability of the event W

Question 5

Use classical probability to determine the probability of choosing a day of the week that begins with the letter "S."

A)
B)
C)
D)

Question 6

What is the probability of flipping a quarter and a nickel and getting heads on both coins or getting tails on both coins?

A)
B)
C)
D)1

Question 7

For probability purposes,an experiment is ________.

A)a process that results in some outcome
B)the collection of all possible outcomes
C)a theoretical result
D)the absolute values of all outcomes

Question 8

Probability is ________.

A)the observed result of an experiment
B)the chance that an event will not happen
C)the likelihood that an outcome occurs
D)the number of successes divided by the number of failures

Question 9

Subjective probability ________.

A)can have all probabilities deduced from theoretical arguments because the process that generates the outcomes is known
B)is based on personal judgment
C)is the same as conditional probability
D)is based on experimental data

Question 10

In probability theory,what is the outcome of an experiment?

A)the absolute values of all samples
B)the collection of all possible experiments
C)a theoretical result
D)the result that is observed

Question 11

The probability of Barack hitting a homerun is one chance in fifty.What is the probability that he will not hit a homerun?

A)98%
B)
C)49%
D)unknown since the events are mutually exclusive

Question 12

The probability of the event A,at least fifty people will show up for traffic court today,is 35%.What is the probability of the complement of A?

A)85%
B)35%
C)15%
D)65%

Question 13

A statement made by experts on a TV show that the Michigan Tech Huskies men's hockey team has one chance in four of winning the NCAA Frozen Four in 2014 is an example of ________.

A)subjective probability
B)relative frequency probability
C)classical probability
D)conditional probability

Question 14

Relative frequency probability ________.

A)is based on empirical data
B)is based on theoretical arguments
C)is the same as subjective probability
D)is based on personal judgment

Question 15

Two fair coins,one quarter and one nickel,are being flipped.Identify the correct statement from the following.

A)An event in this case would be flipping only the quarter twice.
B)Both coins will not yield the same result.
C)The sample space in this case would be heads/heads,heads/tails,tails/heads,and tails/tails.
D)The only possible outcome in this case is getting heads for the quarter and tails for the nickel.

Question 16

In probability theory,an event is ________.

A)a process that results in some outcome
B)a collection of one or more outcomes from a sample space
C)a theoretical result
D)the absolute values of all outcomes

Question 17

What is sample space?

A)the collection of all possible outcomes
B)a process that results in some outcome
C)a theoretical result
D)the absolute values of all outcomes/the likelihood of an outcome

Question 18

Since there are seven days in a week,there is a 14% chance that a meeting will be held on a Monday.This is an application of the ________ definition of probability.

A)relative frequency
B)classical
C)subjective
D)conditional

Question 19

According to historical data,there are 300 days of sun in Colorado Springs each year.This suggests that the probability of a sunny day in 2013 is = 82%.This is an application of ________.

A)conditional probability
B)subjective probability
C)classical probability
D)relative frequency probability

Question 20

There are four slices of pepperoni pizza and three slices of veggie pizza sitting on the counter.What is the probability of randomly choosing a slice of veggie pizza?

A)
B)
C)
D)

Question 21

Two events are independent if ________.

A)the probability of one or both events is greater than one
B)the probability of each event is not affected by the other
C)the probability of one event prohibits the occurrence of the other
D)the two events occur at the same time

Question 22

There are four mammals (one dog and three cats)and three reptiles (one snake and two turtles)on sale at a drastic discount at the local pet store.What is the probability that the first two animals sold are both cats?

A)
B)
C)
D)

Question 23

What is the probability of flipping a quarter three times and getting tails all three times?

A)
B)
C)
D)

Question 24

Given the probability of event G is ,the probability of event H is ,the probability of both events G and H is = .This is an example of the two events being ________.

A)dependent
B)independent
C)mutually exclusive
D)exhaustive

Question 25

A continuous random variable is ________.

A)a variable for which the number of possible outcomes can be counted
B)a variable that has outcomes over one or more intervals of real numbers
C)a characterization of the possible values that a random variable may assume along with the probability of each value
D)a variable for which there is only one possible value

Question 26

The likelihood that an individual prefers a Ford Mustang convertible is based on the proportion of the population that prefers a Ford Mustang that also prefers a convertible.This is an example of ________.

A)conditional probability
B)generic probability
C)independent probability
D)mutually exclusive probability

Question 27

Which of the following is true of random variables?

A)Random variables may not have a physical or natural meaning.
B)Random variables are used with data that is numerical.
C)Each element in a sample space is represented by a random variable.
D)The probability of the occurrence of an event is represented by a random variable.

Question 28

Conditional probability is the probability of ________.

A)the occurrence of one event given that another event has already occurred
B)the occurrence of two events that are mutually exclusive
C)the occurrence of the complement of an event
D)two events occurring at the same time

Question 29

A discrete random variable is ________.

A)a variable that has outcomes over one or more continuous intervals of real numbers
B)a characterization of the possible values that a random variable may assume along with the probability of each value
C)a variable for which the number of possible outcomes can be counted
D)a variable for which there is only one possible value

Question 30

For a discrete random variable A,the probability distribution of the discrete outcomes is called a ________.

A)conditional mass function,c(a)
B)cumulative frequency function,m(a)
C)probability mass function,f(a)
D)discrete value function,d(a)

Question 31

A random variable is a function that assigns a real number to ________.

A)each event in a sample space
B)each outcome within a sample space
C)each experiment in a sample space
D)each sample space within the universe

Question 32

All of the following are continuous random variables except ________.

A)the number of tires on the next vehicle in the Taco Bell drive-through
B)the daily change in the Dow Jones Industrial Average
C)the height of the next customer in the Kings Sooper checkout line
D)the temperature on Thanksgiving Day

Question 33

All of the following are examples of discrete random variables except ________.

A)the income of an American family
B)the outcomes from rolling dice
C)the rating of customer satisfaction on a scale of 1 to 10
D)the number of apples in a basket

Question 34

Consider the following table that shows the details of the people applying for a particular job.The cell numbers indicate the number of applicants belonging to a particular age group and gender. What is the probability that a female or someone less than 41 years old is chosen?

A)
B)
C)
D)

Question 35

At the Simple Sub Shop,there are five types of sandwiches and three different beverages.Lunch Special A consists of a club sandwich and a cola.What is the probability that someone would choose a sandwich and a beverage at random and end up with Lunch Special A?

A)
B)
C)
D)

Question 36

In an experiment,a random variable is ________.

A)a value picked from a set of values that all have an equal chance of occurring
B)a variable chosen at random from a distribution list
C)an outcome that has zero chances of occurring
D)a numerical description of the outcome of an experiment

Question 37

Which of the following cannot be used to develop a probability distribution?

A)listing the probabilities for the outcomes of rolling two dice
B)measuring the frequency of low and high temperatures for the month of November
C)stating that there is a definite chance of rain tomorrow
D)surveying sports experts at the beginning of the season on the odds of the Colorado Rockies winning the World Series

Question 38

Two events are mutually exclusive as long as ________.

A)they can occur simultaneously
B)they have two outcomes in common
C)they have no outcomes in common
D)between them,they account for every event in the sample space

Question 39

Five identical boxes are kept with different amounts of money in them.It is known that they contain $5,$10,$15,$20,and $50,although it is not clear which box contains what amount of money.What is the chance of choosing a box that contains either an amount greater than $10 or an amount that is evenly divisible by ten?

A)
B)
C)
D)

Question 40

The law of probability that is used to calculate conditional probability is called ________.

A)the addition law
B)the multiplication law
C)the conditional law
D)the law of independence

Question 41

All of the following are true about the binomial distribution except ________.

A)for values of p larger than 0.5,the distribution is negatively skewed
B)for values of p smaller than 0.5,the distribution is positively skewed
C)for p = 1.0,the distribution is nearly normal
D)for p = 0.5,the distribution is symmetric

Question 42

The curve that characterizes outcomes of a continuous random variable is called a ________.

A)cumulative distribution function,c(x)
B)probability mass function,p(x)
C)continuous random function,r(x)
D)probability density function,f(x)

Question 43

Given that a binomial distribution models n independent replications each with a probability p of success,the expected value of the distribution is ________.

A)n(1 - p)
B)np(1 - p)
C)np
D)np(n)

Question 44

Over time,it's been found that 45% of customers at Daily Dose buy the Deluxe Joe.What is the probability that out of the next 10 customers,exactly five will buy the Deluxe Joe?

A)1.85%
B)100%
C)23.4%
D)98.16%

Question 45

For a fund raiser,the local chapter of Pie Eaters Anonymous is offering a set of silver pie pans worth $1000.Each of the 1200 raffle tickets cost $2.What is the expected value for this raffle?

A)-$1.17
B)$2
C)$1400
D)-$0.01

Question 46

A binomial distribution models several independent replications of a ________.

A)probability density function
B)Bernoulli experiment
C)continuous distribution
D)Poisson experiment

Question 47

The expected value of a random variable corresponds to the notion of the ________ of a sample.

A)median
B)mode
C)mean
D)range

Question 48

Continuous probability distributions depend on all of the following parameters except a ________.

A)location parameter
B)scale parameter
C)formal parameter
D)shape parameter

Question 49

At a particular toll booth,20% of vehicles use transponders while the rest have their license plates scanned.Usually,150 vehicles pass this toll booth during any one hour time period.During the next hour,what is the probability that 20 or less vehicles will pass through using a transponder?

A)1.34%
B)0.08%
C)3.53%
D)98.65%

Question 50

The Bernoulli distribution characterizes a random variable having two possible outcomes each with a ________.

A)varying probability of occurrence
B)continuous probability of occurrence
C)constant probability of occurrence
D)conditional probability of occurrence

Question 51

The Poisson distribution is a version of the discrete distribution used ________.

A)to adjust for the likelihood of one event occurring most of the time
B)as a complement to the Bernoulli distribution
C)to measure the number of events occurring in an interval of time
D)to simulate a continuous distribution

Question 52

At a particular toll booth,20% of vehicles use transponders while the rest have their license plates scanned.Usually,150 vehicles pass this toll booth during any one hour time period.During the next hour,what is the probability that exactly 25 vehicles will pass through using a transponder?

A)20.84%
B)86.33%
C)5.11%
D)4.54%

Question 53

At a particular toll booth,20% of vehicles use transponders while the rest have their license plates scanned.Usually,150 vehicles pass this toll booth during any one hour time period.During the next hour,what is the probability that more than 40 vehicles will pass through using a transponder?

A)3.23%
B)6.17%
C)1.85%
D)96.77%

Question 54

The probability that a random variable in a continuous probability distribution will assume a value between a and b is given by ________.

A)the area above the function curve between two boundary values a and b
B)the width of the function curve between two boundary values a and b
C)the area beneath the function curve between two boundary values a and b
D)the height of the function curve between two boundary values a and b

Question 55

A cumulative distribution function,F(x),is a probability distribution in which ________.

A)the probability of random variable X is a fixed constant
B)the probability of random variable X is for a value less than or equal to a specified value,x
C)the total of the probabilities of all outcomes totals between 1 and 2
D)the probability of random variable X is for a value greater than or equal to a specified value,x

Question 56

Which of the following can be modeled using a Bernoulli distribution?

A)a survey question where an individual responds yes or no
B)the highest recorded temperature in the month of June
C)the number of errors per product produced
D)the average number of consumers in a restaurant

Question 57

All of the following are true about a probability density function,f(x),except ________.

A)f(x)≥ 0 for all values of x
B)the total area under the function above the x-axis is 1.0
C)the probability distribution will approach the shape of a smooth curve
D)the probability will assume a value greater than or equal to a specified value,x

Question 58

The Poisson distribution might be used to model all of the following except ________.

A)the number of errors per line in software code
B)the number of customers that use an ATM during lunch hour
C)the number of items ordered per customer from inventory
D)the number of voters registered for an upcoming election

Question 59

A continuous random variable defined over one or more intervals of real numbers can have ________.

A)a fixed number of possible outcomes
B)values that are between 0 and 1 only
C)an infinite number of possible outcomes
D)values that have no physical or natural meaning

Question 60

Given that a binomial distribution models n independent replications each with a probability p of success,the variance of the distribution is ________.

A)np
B)np(n)
C)np(1 - p)
D)n(1 - p)

Question 61

For a normal distribution,as μ changes,________.

A)the density of the function increases
B)the median remains unchanged
C)the distribution becomes wider
D)the location of the distribution on the x-axis changes

Question 62

What is the likelihood of finding a price between $3.80 and $3.85 for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.

A)0.3413
B)0.4641
C)0.2638
D)0.5746

Question 63

Which of the following is not true of the exponential distribution?

A)The exponential distribution has two parameters,λ and ε.
B)The exponential distribution models the time between randomly occurring events.
C)For the exponential distribution,the current time has no effect on future outcomes.
D)The exponential distribution has its greatest density at 0.

Question 64

What is the likelihood of finding a price of $3.68 or less for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.

A)0.4772
B)0.0793
C)0.4207
D)0.0228

Question 65

For the standard normal distribution,the scale along the z-axis represents ________.

A)the probable values of the mean
B)the range of the distribution
C)the number of standard deviations from the mean
D)the possible values of the median of the distribution

Question 66

The standard normal distribution is a special case of the normal distribution in which ________.

A)the mean = 0 and the variance = 0
B)the mean = 1 and the variance = 1
C)the mean = 1 and the variance = 0
D)the mean = 0 and the variance = 1

Question 67

What is the likelihood of finding a price between $3.71 and $3.85 for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.

A)0.4974
B)0.9948
C)0.8385
D)0.2487

Question 68

The normal continuous probability distribution is characterized by two parameters,________.

A)the mean,μ,and the median
B)the median and the standard deviation,σ
C)the mean,μ,and the variance,σ²
D)the mode and the range

Question 69

Which of the following is not true for a normal distribution?

A)The curve for a normal distribution is symmetric.
B)One-third of the total area falls above the mean.
C)The tails of the distribution extend to negative and positive infinity.
D)99% of the area lies within 3 standard deviations of the mean.

Question 70

Families with an income range of $35,000 to $55,000 are likely to buy the latest Star Quest DVD.What is the expected value for the family income for this uniform probability distribution?

A)$45,000
B)$90,000
C)$20,000
D)$1666.67

Question 71

Which of the following is true of the triangular distribution?

A)The expected value of the triangular distribution is given by (a + b)/2.
B)The triangular distribution is a bounded distribution.
C)The triangular distribution has only one parameter λ.
D)All the outcomes in the distribution have the same chance of occurrence.

Question 72

For a uniform continuous probability distribution,all outcomes between minimum value a and maximum value b ________.

A)are unknown
B)have a probability lesser than 0
C)are equally likely
D)are difficult to measure

Question 73

All of the following are continuous probability distributions that can be matched to specific empirical data except ________.

A)the Bernoulli distribution
B)the Pareto distribution
C)the lognormal distribution
D)the geometric distribution

Question 74

A joint probability distribution describes the probabilities of outcomes ________.

A)of two different random variables occurring at the same time
B)of the same random variable measured at two different time periods
C)of two different random variables occurring sequentially
D)of two random variables measured in two different time periods

Question 75

For the normal continuous probability distribution,as σ² increases,the distribution ________.

A)becomes more narrow
B)becomes wider
C)remains unchanged
D)becomes asymmetric

Question 76

Families with an income range of $35,000 to $55,000 are likely to buy the latest Star Quest DVD.What is the variance for this uniform probability distribution of family income?

A)$675,000,000
B)$200,000,000
C)$33,333,333
D)$1666.67

Question 77

What is the likelihood of finding a price between $3.68 and $3.85 for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.

A)0.058
B)0.8965
C)1.0
D)0.2257

Question 78

The expected value of the exponential distribution is ________.

A)
B)E
C)
D)ln e

Question 79

Which of the following is true for continuous probability distributions?

A)P(a < X < b)is the same as P(a > X > b)
B)P(a ≤ X ≤ b)is the same as P(a < X < b)
C)P(a ≥ X ≥ b)is the same as P(a < X < b)
D)P(a = X = b)is the same as P(a < X < b)

Question 80

What is the likelihood of finding a price of $3.85 or more for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.

A)0.0808
B)0.4192
C)0.3508
D)0.1492