Question 1

​An insurance company needs to determine the annual premium required to break even on fire protection policies with a face value of $80,000.If x is the claim size on these policies and the analysis is restricted to the losses $20,000,$70,000,and $80,000,then the probability distribution of x is as shown in the table.What premium should customers be charged for the company to break even? Round your answer to the nearest dollar.​ ​

Accepted Answer

A)  ​$202 
B)  ​$14 
C)  ​$42,500 
D)  ​$203 
E)  ​$40,600

Question 2

Sketch a graph of the probability distribution. ​

Accepted Answer

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

Question 3

​A baseball fan examined the record of a favorite baseball player's performance during his last 50 games.The numbers of games in which the player had zero,one,two,three,and four hits are recorded in the table shown below.Find the standard deviation .Round your answer to two decimal places.

Accepted Answer

A)  ​1.36 
B)  ​1.13 
C)  ​1.61 
D)  ​1.27 
E)  ​1.17

Question 4

​If X is an exponential random variable with the probability density function  ,find E(X). ​

Accepted Answer

A)  ​10 
B)  ​5 
C)  ​  
D)  ​  
E)  ​1

Question 5

​Find the mean,variance,and standard deviation of the uniform distribution  over the interval [0,26] without using integration. ​

Accepted Answer

A)  ​expected value (mean): 13
Variance: 56.333
Standard deviation: 7.506
​ 
B)  ​expected value (mean): 56.333
Variance: 13
Standard deviation: 7.506
​ 
C)  ​expected value (mean): 56.333
Variance: 7.506
Standard deviation: 13
​ 
D)  ​expected value (mean): 7.506
Variance: 13
Standard deviation: 56.333 
E)  ​expected value (mean): 13
Variance: 7.506
Standard deviation: 56.333

Question 6

​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)  ​0.3085 
B)  ​0.2525 
C)  ​0.1908 
D)  ​0.1223 
E)  ​0.1695

Question 7

​Find the mean and median of  ​

Accepted Answer

A)  ​mean: 24.00
Median: 24.00 
B)  ​mean: 24.00
Median: 0.17 
C)  ​mean: 4.00
Median: 0.50 
D)  ​mean: 6.00
Median: 6.00 
E)  ​mean: 0.50
Median: 0.50

Question 8

​The time t (in hours)required for a new employee to successfully learn to operate a machine in a manufacturing process is described by the probability density function  over the interval  Find the probability that a new employee will learn to operate the machine in more than 4 hours but less than 7 hours.Round your answer to four decimal places. ​

Accepted Answer

A)  ​0.5371 
B)  ​0.1583 
C)  ​0.4632 
D)  ​0.1469 
E)  ​0.3162

Question 9

​Find the median of the exponential probability density function  over the interval [0,∞).Round your answer to three decimal places. ​​

Accepted Answer

A)  ​0.52 
B)  ​0.693 
C)  ​0.924 
D)  ​0.455 
E)  ​0.375

Question 10

​Estimate the variance for the following probability distribution to two decimal places. ​
​

Accepted Answer

A)  ​2.00 
B)  ​1.40 
C)  ​1.18 
D)  ​1.96 
E)  ​1.00

Question 11

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

Accepted Answer

A)  ​ 
​
Mean: 2.012
​ 
B)  ​ 
​
Mean: 0.555
​ 
C)  ​ 
​
Mean: 1.848
​ 
D)  ​ 
​
Mean: 0.714
​ 
E)  ​ 
​
Mean: 1.6
​

Question 12

If x is the net gain to a player in a game of chance,then E(x)is usually negative.This value gives the average amount per game the player can expect to lose over the long run.A service organization is selling $2 raffle tickets as part of a fundraising program.The first prize is a boat valued at $2910,and the second prize is a camping tent valued at $400.In addition to the first and second prizes,there are twenty $24 gift certificates to be awarded.The number of tickets sold is 3000.Find the expected net gain to the player for one play of the game.Round your answer to the nearest cent. ​

Accepted Answer

A)  ​$1,109.33 
B)  ​$1.34 
C)  ​$0.74 
D)  ​-$0.74 
E)  ​-$1,109.33

Question 13

Find the mean,variance,and standard deviation of the normal density function   Do not use integration. ​

Accepted Answer

A)  expected value (mean): -3
Variance: 36
Standard deviation: 6
​ 
B)  expected value (mean): 36
Variance: -3
Standard deviation: 6
​ 
C)  expected value (mean): 36
Variance: 6
Standard deviation: -3
​ 
D)  expected value (mean): 6
Variance: -3
Standard deviation: 36
​ 
E)  expected value (mean): -3
Variance: 6
Standard deviation: 36
​

Question 14

A coin is tossed three times.Describe the event A that at least two tails occur. ​

Accepted Answer

A)  ​{TTT, THH, THT, HHT} 
B)  ​{HHH, TTH, THT, HTT} 
C)  ​{TTT, TTH, THT, HTT} 
D)  ​{TTTT, TTHT, THTT, HTTT} 
E)  ​{TT,HT,TH}

Question 15

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

Accepted Answer

A)  ​0.11 
B)  ​0.75 
C)  ​0.94 
D)  ​0.13 
E)  ​0.08

Question 16

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

Accepted Answer

A)  ​0.063 
B)  ​0.27 
C)  ​0.149 
D)  ​0.2 
E)  ​0.189

Exam 9: Probability and Calculus

Sketch a graph of the probability distribution.

A baseball fan examined the record of a favorite baseball player's performance during his last 50 games.The numbers of games in which the player had zero,one,two,three,and four hits are recorded in the table shown below.Find the standard deviation .Round your answer to two decimal places.

If X is an exponential random variable with the probability density function ,find E(X) .

Find the mean,variance,and standard deviation of the uniform distribution over the interval [0,26] without using integration.

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 mean and median of

Find the median of the exponential probability density function over the interval [0,∞) .Round your answer to three decimal places.

Estimate the variance for the following probability distribution to two decimal places.

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

Find the mean,variance,and standard deviation of the normal density function Do not use integration.

A coin is tossed three times.Describe the event A that at least two tails occur.

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

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

Exam 9: Probability and Calculus

Sketch a graph of the probability distribution. ​

​A baseball fan examined the record of a favorite baseball player's performance during his last 50 games.The numbers of games in which the player had zero,one,two,three,and four hits are recorded in the table shown below.Find the standard deviation .Round your answer to two decimal places.

​If X is an exponential random variable with the probability density function ,find E(X) . ​

​Find the mean,variance,and standard deviation of the uniform distribution over the interval [0,26] without using integration. ​

​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 mean and median of ​

​Find the median of the exponential probability density function over the interval [0,∞) .Round your answer to three decimal places. ​​

​Estimate the variance for the following probability distribution to two decimal places. ​ ​

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

Find the mean,variance,and standard deviation of the normal density function Do not use integration. ​