Question 1

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?

Accepted Answer

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

Question 2

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?

Accepted Answer

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 3

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?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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

Accepted Answer

The answer of James has two fair coins. When he...

Question 7

Which of the following is a discrete random variable?

Accepted Answer

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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

The center of a normal curve is

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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.

Exam 5: Probability: an Introduction to Modeling Uncertainty

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?

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

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

Which of the following is a discrete random variable?

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

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

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

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

The center of a normal curve is

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

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

Exam 5: Probability: an Introduction to Modeling Uncertainty

What is the mean of x, given the exponential probability function f(x) =120ex20 for x≥0 ? f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }f(x) =201​e20x​ for x≥0 ?

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

Which of the following is a discrete random variable?

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

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

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

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

The center of a normal curve is

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

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

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