Deck 5: Probability: an Introduction to Modeling Uncertainty

Question 1

The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X.

A)2.887
B)3.464
C)8.333
D)12

Answer 1

2.887

Question 2

A __________ describes the range and relative likelihood of all possible values for a random variable.

A)probability distribution for a random variable
B)probability mass function of an event
C)density function
D)probability

Answer 2

probability distribution for a random variable

Question 3

The __________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour.

A)binomial
B)normal
C)triangular
D)Poisson

Answer 3

Poisson

Question 4

A joint probability is the

A)sum of the probabilities of two events.
B)probability of the intersection of two events.
C)probability of the union of two events.
D)sum of the probabilities of two independent events.

Question 5

Which of the following is a discrete random variable?

A)The number of times a student guesses the answers to questions on a certain test
B)The amount of gasoline purchased by a customer
C)The amount of mercury found in fish caught in the Gulf of Mexico
D)The height of water-oak trees

Question 6

If a z-score is zero, then the corresponding x-value must be equal to the

A)mean.
B)median.
C)mode.
D)standard deviation.

Question 7

An initial estimate of the probabilities of events is a __________ probability.

A)posterior
B)conditional
C)empirical
D)prior

Question 8

A variable that can only take on specific numeric values is called a

A)categorical variable.
B)discrete random variable.
C)continuous random variable.

Question 9

The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution.

A)4
B)5
C)6
D)7

Question 10

All the events in the sample space that are not part of the specified event are called

A)joint events.
B)the complement of the event.
C)simple events.
D)independent events.

Question 11

Two events are independent if

A)the two events occur at the same time.
B)the probability of one or both events is greater than 1.
C)P(A | B) = P(A) or P(B | A) = P(B).
D)None of these are correct.

Question 12

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

A)discrete random variable.
B)continuous random variable.
C)complex random variable.
D)categorical random variable.

Question 13

Which statement is true about mutually exclusive events?

A)If events A and B cannot occur at the same time, they are called mutually exclusive.
B)If either event A or event B must occur, they are called mutually exclusive.
C)P(A) + P(B) = 1 for any events A and B that are mutually exclusive.
D)None of these are correct.

Question 14

Bayes' theorem is a method used to compute __________ probabilities.

A)posterior
B)conditional
C)empirical
D)prior

Question 15

All of the following are examples of discrete random variables except

A)number of tickets sold.
B)marital status.
C)time.
D)population of a city.

Question 16

In the probability table below, which value is a marginal probability? ​
Completed
Obstacle Course Level
No
Yes
Total
Challenging
0)4
0)3
0)7
Easy
0)1
0)2
0)3
Total
0)5
0)5
1)0

A)0.1
B)1.0
C)0.5
D)0.4

Question 17

Probability is the

A)number of successes divided by the number of failures.
B)numerical measure of the likelihood that an event will occur.
C)chance that an event will not happen.
D)number of successes divided by the standard deviation of the distribution.

Question 18

Sample space is

A)a process that results in some outcome.
B)the collection of all possible outcomes.
C)the collection of events
D)a subgroup of a population/the likelihood of an outcome.

Question 19

The event containing the outcomes belonging to A or B or both is the __________ of A and B.

A)union
B)Venn diagram
C)intersection
D)complement

Question 20

Which of the following statements is correct?

A)The binomial and normal distributions are both discrete probability distributions.
B)The binomial and normal distributions are both continuous probability distributions.
C)The binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution.
D)The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

Question 21

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution?

A)7,533
B)8,078
C)10,000
D)12,467

Question 22

The center of a normal curve is

A)always equal to zero.
B)the mean of the distribution.
C)always a positive number.
D)equal to the standard deviation.

Question 23

What is the total area under the normal distribution curve?

A)It depends upon the mean and standard deviation
B)It must be calculated
C)1
D)100

Question 24

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better?

A)0.6%
B)2.5%
C)6%
D)25%

Question 25

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive-thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order?

A)0.1813
B)0.4866
C)0.6321
D)0.7769

Question 26

The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probability that Samantha has to wait less than 4.5 minutes to catch the bus?

A)10%
B)20%
C)30%
D)3%

Question 27

James has two fair coins. When he flips them, what is the sample space?

Question 28

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50^th percentile of this distribution?

A)75
B)85
C)95
D)105

Question 29

The triangular distribution is a good model for __________ distributions.

A)uniform
B)skewed
C)normal

Question 30

In a normal distribution, which is greater, the mean or the median?

A)Mean
B)Median
C)Neither the mean or the median (they are equal)
D)Cannot be determined with the information provided

Question 31

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the days does he exceed 13,000 steps?

A)2.28%
B)5%
C)95%
D)97.72%

Question 32

Which of the following is not a characteristic of the normal probability distribution?

A)The mean, median, and the mode are equal.
B)The mean of the distribution can be negative, zero, or positive.
C)The distribution is symmetrical.
D)The standard deviation must be 1.

Question 33

A survey of 100 random high school students finds that 85 students watched the Super Bowl, 25 students watched the Stanley Cup Finals, and 20 students watched both games. How many students did not watch either game?

A)15
B)30
C)10
D)20

Question 34

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

A)95%
B)97.7%
C)99.7%
D)100%

Question 35

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?

A) $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$
B) $f ( x ) = \frac { 1 } { 3 } e ^ { - \frac { x } { 3 } }$
C) $f ( x ) = \frac { 2 } { 3 } e ^ { - \frac { 2 } { 3 } x }$
D)None of these are correct.

Question 36

What is the mean of x, given the exponential probability function $$f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$$

A)0.05
B)20
C)100
D)2,000