Question 1

​Find   given the probability distribution. ​​

Accepted Answer

A)  ​0.440 
B)  ​1.000 
C)  ​0.792 
D)  ​0.648 
E)  ​0.250 
A)  ​0.440 
B)  ​1.000 
C)  ​0.792 
D)  ​0.648 
E)  ​0.250 D

Question 2

​For the probability density function   on the interval   find the probability that   Round your answer to the nearest hundredth. ​

Accepted Answer

A)  ​0.17 
B)  ​0.6 
C)  ​0.8 
D)  ​0.4 
E)  ​0.13 
A)  ​0.17 
B)  ​0.6 
C)  ​0.8 
D)  ​0.4 
E)  ​0.13 C

Question 3

​A meteorologist predicts that the amount of rainfall (in inches)expected for a certain coastal community during a hurricane has the probability density function   ,   Find and interpret the probability   ​

Accepted Answer

A)  17% probability of receiving up to 5 inches of rain 
B)  ​25% probability of receiving up to 5 inches of rain 
C)  ​30% probability of receiving up to 5 inches of rain 
D)  ​75% probability of receiving up to 5 inches of rain 
E)  ​83% probability of receiving up to 5 inches of rain 
A)  17% probability of receiving up to 5 inches of rain 
B)  ​25% probability of receiving up to 5 inches of rain 
C)  ​30% probability of receiving up to 5 inches of rain 
D)  ​75% probability of receiving up to 5 inches of rain 
E)  ​83% probability of receiving up to 5 inches of rain B

Question 4

​Find the constant k such that the function   is a probability density function over the interval [0,∞]. ​

Accepted Answer

A)  1​ 
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  1​ 
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 5

​Find the constant k such that the function   is a probability density function over the interval [3,8]. ​

Accepted Answer

A)  ​5 
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​5 
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 6

​The daily demand x for a certain product (in hundreds of pounds)is a random variable with the probability density function   over the interval [0,6].Find the probability that x is within one standard deviation of the mean.Express your answer as a percent.Round to two decimal places. ​

Accepted Answer

A)  ​96.42% 
B)  ​49.35% 
C)  ​62.61% 
D)  ​13.44% 
E)  ​72.77% 
A)  ​96.42% 
B)  ​49.35% 
C)  ​62.61% 
D)  ​13.44% 
E)  ​72.77%

Question 7

​Find  given the probability distribution. ​
​

Accepted Answer

A)  ​0.320 
B)  ​0.480 
C)  ​0.520 
D)  ​0.800 
E)  ​0.200 
A)  ​0.320 
B)  ​0.480 
C)  ​0.520 
D)  ​0.800 
E)  ​0.200

Question 8

​A publishing company introduces a new weekly magazine that sells for $4.65 on the newsstand.The marketing group of the company estimates that sales x (in thousands)will be approximated by the following probability function.Find the expected revenue.Round your answer to the nearest dollar. ​​

Accepted Answer

A)  ​$96,255 
B)  ​$96 
C)  ​$491 
D)  ​$20,700 
E)  ​$490,622 
A)  ​$96,255 
B)  ​$96 
C)  ​$491 
D)  ​$20,700 
E)  ​$490,622

Question 9

​Find the standard deviation σ for the following probability distribution.Round your answer to three decimal places. ​​

Accepted Answer

A)  ​3.200 
B)  ​1.720 
C)  ​8.762 
D)  ​2.960 
E)  ​1.789 
A)  ​3.200 
B)  ​1.720 
C)  ​8.762 
D)  ​2.960 
E)  ​1.789

Question 10

​Sketch the graph of the probability density function   over the interval   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 11

​The daily demand for gasoline (in millions of gallons)in a city is described by the probability density function   over the interval   Find the probability that the daily demand for gasoline will be at least 2 million gallons.Round your answer to three decimal places. ​

Accepted Answer

A)  ​0.563 
B)  ​0.063 
C)  ​0.141 
D)  ​0.391 
E)  ​0.25 
A)  ​0.563 
B)  ​0.063 
C)  ​0.141 
D)  ​0.391 
E)  ​0.25

Question 12

​A card is chosen at random from three 52-card decks of standard playing cards.What is the probability that the card will be black and a face card? A face card is a king,a queen,or a jack. ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 13

​For the given probability density function,find Var(X).Round your answer to three decimal places. ​
​   ​

Accepted Answer

A)  ​12 
B)  ​6.4 
C)  ​9 
D)  ​5.4 
E)  ​28.8 
A)  ​12 
B)  ​6.4 
C)  ​9 
D)  ​5.4 
E)  ​28.8

Question 14

Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S. ​

Accepted Answer

A)  {OOO, OOU, OUO, UOO, UUU, UUO, UOU} 
B)  {OOO, OOU, UOO, UUU, UUO, UOU, OUU} 
C)  {OOO, OOU, OUO, UOO, UUO, UOU, OUU} 
D)  {OOO, OUO, UOO, UUO, UOU, OUU} 
E)  {OOO,OOU,OUO,UOO,UUU,UUO,UOU,OUU} 
A)  {OOO, OOU, OUO, UOO, UUU, UUO, UOU} 
B)  {OOO, OOU, UOO, UUU, UUO, UOU, OUU} 
C)  {OOO, OOU, OUO, UOO, UUO, UOU, OUU} 
D)  {OOO, OUO, UOO, UUO, UOU, OUU} 
E)  {OOO,OOU,OUO,UOO,UUU,UUO,UOU,OUU}

Question 15

​Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is   on the interval   Find the probability that the person will wait no longer than 5 minutes. ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 16

​Let x be a random variable that is normally distributed with the given mean   and standard deviation   Find the probability   using a symbolic integration utility.Round your answer to four decimal places. ​

Accepted Answer

A)  ​0.6687 
B)  ​0.797 
C)  ​0.5889 
D)  ​0.5292 
E)  ​0.5359 
A)  ​0.6687 
B)  ​0.797 
C)  ​0.5889 
D)  ​0.5292 
E)  ​0.5359

Question 17

​Find the value of the constant a that makes the given function a probability density function on the stated interval.   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​1 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​1

Question 18

Find the expected value E(x)for the following probability distribution.Round your answer to three decimal places. ​​

Accepted Answer

A)  ​9.061 
B)  ​841.659 
C)  ​6,740.410 
D)  ​708,389.590 
E)  ​82.100 
A)  ​9.061 
B)  ​841.659 
C)  ​6,740.410 
D)  ​708,389.590 
E)  ​82.100

Question 19

​Sketch the graph of the following probability density function and locate the mean on the graph. ​
​   ​
​

Accepted Answer

A)  ​  
​
Mean: 2 
B)  ​  
​
Mean: 3 
C)  ​  
​
Mean: 4​ 
D)  ​  
​
Mean: 4 
E)  ​  
​
Mean: 1.5 
A)  ​  
​
Mean: 2 
B)  ​  
​
Mean: 3 
C)  ​  
​
Mean: 4​ 
D)  ​  
​
Mean: 4 
E)  ​  
​
Mean: 1.5

Question 20

​Determine whether the table represents a probability distribution ?

Accepted Answer

A) True 
 B)False

Find given the probability distribution.

For the probability density function on the interval find the probability that Round your answer to the nearest hundredth.

A meteorologist predicts that the amount of rainfall (in inches)expected for a certain coastal community during a hurricane has the probability density function , Find and interpret the probability

Find the constant k such that the function is a probability density function over the interval [0,∞].

Find the constant k such that the function is a probability density function over the interval [3,8].

The daily demand x for a certain product (in hundreds of pounds)is a random variable with the probability density function over the interval [0,6].Find the probability that x is within one standard deviation of the mean.Express your answer as a percent.Round to two decimal places.

Find given the probability distribution.

A publishing company introduces a new weekly magazine that sells for $4.65 on the newsstand.The marketing group of the company estimates that sales x (in thousands)will be approximated by the following probability function.Find the expected revenue.Round your answer to the nearest dollar.

Find the standard deviation σ for the following probability distribution.Round your answer to three decimal places.

Sketch the graph of the probability density function over the interval

The daily demand for gasoline (in millions of gallons)in a city is described by the probability density function over the interval Find the probability that the daily demand for gasoline will be at least 2 million gallons.Round your answer to three decimal places.

A card is chosen at random from three 52-card decks of standard playing cards.What is the probability that the card will be black and a face card? A face card is a king,a queen,or a jack.

For the given probability density function,find Var(X).Round your answer to three decimal places.

Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S.

Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is on the interval Find the probability that the person will wait no longer than 5 minutes.

Let x be a random variable that is normally distributed with the given mean and standard deviation Find the probability using a symbolic integration utility.Round your answer to four decimal places.

Find the value of the constant a that makes the given function a probability density function on the stated interval.

Find the expected value E(x)for the following probability distribution.Round your answer to three decimal places.

Sketch the graph of the following probability density function and locate the mean on the graph.

Determine whether the table represents a probability distribution ?

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Series and Taylor Polynomials

Differential Equations

Filters

Exam 9: Probability and Calculus

​Find given the probability distribution. ​​

​For the probability density function on the interval find the probability that Round your answer to the nearest hundredth. ​

​A meteorologist predicts that the amount of rainfall (in inches)expected for a certain coastal community during a hurricane has the probability density function , Find and interpret the probability ​

​Find the constant k such that the function is a probability density function over the interval [0,∞]. ​

​Find the constant k such that the function is a probability density function over the interval [3,8]. ​

​The daily demand x for a certain product (in hundreds of pounds)is a random variable with the probability density function over the interval [0,6].Find the probability that x is within one standard deviation of the mean.Express your answer as a percent.Round to two decimal places. ​

​Find given the probability distribution. ​ ​

​A publishing company introduces a new weekly magazine that sells for $4.65 on the newsstand.The marketing group of the company estimates that sales x (in thousands)will be approximated by the following probability function.Find the expected revenue.Round your answer to the nearest dollar. ​​

​Find the standard deviation σ for the following probability distribution.Round your answer to three decimal places. ​​

​Sketch the graph of the probability density function over the interval ​

​The daily demand for gasoline (in millions of gallons)in a city is described by the probability density function over the interval Find the probability that the daily demand for gasoline will be at least 2 million gallons.Round your answer to three decimal places. ​

​A card is chosen at random from three 52-card decks of standard playing cards.What is the probability that the card will be black and a face card? A face card is a king,a queen,or a jack. ​

​For the given probability density function,find Var(X).Round your answer to three decimal places. ​ ​ ​

Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S. ​

​Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is on the interval Find the probability that the person will wait no longer than 5 minutes. ​

​Let x be a random variable that is normally distributed with the given mean and standard deviation Find the probability using a symbolic integration utility.Round your answer to four decimal places. ​

​Find the value of the constant a that makes the given function a probability density function on the stated interval. ​

Find the expected value E(x)for the following probability distribution.Round your answer to three decimal places. ​​

​Sketch the graph of the following probability density function and locate the mean on the graph. ​ ​ ​ ​

​Determine whether the table represents a probability distribution ?

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Series and Taylor Polynomials

Differential Equations

Filters

Find given the probability distribution.

For the probability density function on the interval find the probability that Round your answer to the nearest hundredth.

A meteorologist predicts that the amount of rainfall (in inches)expected for a certain coastal community during a hurricane has the probability density function , Find and interpret the probability

Find the constant k such that the function is a probability density function over the interval [0,∞].

Find the constant k such that the function is a probability density function over the interval [3,8].

The daily demand x for a certain product (in hundreds of pounds)is a random variable with the probability density function over the interval [0,6].Find the probability that x is within one standard deviation of the mean.Express your answer as a percent.Round to two decimal places.

Find given the probability distribution.

A publishing company introduces a new weekly magazine that sells for $4.65 on the newsstand.The marketing group of the company estimates that sales x (in thousands)will be approximated by the following probability function.Find the expected revenue.Round your answer to the nearest dollar.

Find the standard deviation σ for the following probability distribution.Round your answer to three decimal places.

Sketch the graph of the probability density function over the interval

The daily demand for gasoline (in millions of gallons)in a city is described by the probability density function over the interval Find the probability that the daily demand for gasoline will be at least 2 million gallons.Round your answer to three decimal places.

A card is chosen at random from three 52-card decks of standard playing cards.What is the probability that the card will be black and a face card? A face card is a king,a queen,or a jack.

For the given probability density function,find Var(X).Round your answer to three decimal places.

Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S.

Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is on the interval Find the probability that the person will wait no longer than 5 minutes.

Let x be a random variable that is normally distributed with the given mean and standard deviation Find the probability using a symbolic integration utility.Round your answer to four decimal places.

Find the value of the constant a that makes the given function a probability density function on the stated interval.

Find the expected value E(x)for the following probability distribution.Round your answer to three decimal places.

Sketch the graph of the following probability density function and locate the mean on the graph.

Determine whether the table represents a probability distribution ?