Question 1

Solve the problem.
-

Accepted Answer

A)  (
A)  4; (
B)  4 
B)  (
A)  2; (
B)  6 
C)  (
A)  1; (
B)  3 
D)  (
A)  2; (
B)  4 
A)  (
A)  4; (
B)  4 
B)  (
A)  2; (
B)  6 
C)  (
A)  1; (
B)  3 
D)  (
A)  2; (
B)  4

Question 2

Solve the problem.
-The shelf life (in days) of a perishable drug is a continuous random variable with probability density function f(x) as shown below.   Find the median shelf life.

Accepted Answer

A)  125 days 
B)  5 days 
C)  15 days 
D)  25 days 
A)  125 days 
B)  5 days 
C)  15 days 
D)  25 days

Question 3

Find the value of the improper integral that converges.
-

Accepted Answer

A)  9 
B)  2 
C)  The improper integral diverges. 
D)    
A)  9 
B)  2 
C)  The improper integral diverges. 
D)

Question 4

Find the probability density function f and the associated cumulative distribution function F for the continuous random
variable X if
-X is uniformly distributed on [1, 7].

Accepted Answer

A)    
B)    7 
C)    
D)    
A)    
B)    7 
C)    
D)

Question 5

X is a continuous random variable with mean µ and standard deviation σ. Find µ and σ, and then find P(µ -σ ≤ X ≤ µ +σ)
if
-X is uniformly distributed on [-6, 6].

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find the median for f(x).
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Find the associated cumulative distribution function. Graph both functions (on separate sets of axes).
-

Accepted Answer

A)  -0.27 
B)  0.38 
C)  -0.62 
D)  0.40 
A)  -0.27 
B)  0.38 
C)  -0.62 
D)  0.40

Question 8

Find a constant k so that kf is a probability density function, or state it does not exist.
-

Accepted Answer

A)    
B)    
C)  k = 6 
D)  does not exist 
A)    
B)    
C)  k = 6 
D)  does not exist

Question 9

Find the value of the improper integral that converges.
-

Accepted Answer

A)  5 
B)    
C)  The improper integral diverges. 
D)    
A)  5 
B)    
C)  The improper integral diverges. 
D)

Question 10

Solve the problem.
-Find the area under the standard normal curve and above the given interval on the horizontal axis.

Accepted Answer

A)  0.0557 
B)  0.4236 
C)  0.4793 
D)  0.5207 
A)  0.0557 
B)  0.4236 
C)  0.4793 
D)  0.5207

Question 11

Find the mean, median, and standard deviation of the continuous random variable X if
-X is an exponential random variable with λ = 2.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Solve the problem.
-The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function f(x) as shown below.   Find the median waiting time. Round to three decimal places.

Accepted Answer

A)  0.693 minutes 
B)  0.143 minutes 
C)  3.892 minutes 
D)  4.852 minutes 
A)  0.693 minutes 
B)  0.143 minutes 
C)  3.892 minutes 
D)  4.852 minutes

Question 13

The quartile points for a probability density function are the values   that divide the area under the graph of the
function into four equal parts. Find the quartile points for the probability density function f(x).
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

F(x) is the cumulative distribution function for a continuous random variable X. Find the probability density function f(x)
associated with F(x).
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Solve the problem.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

X is a continuous random variable with mean   and then find   ) if
-X is uniformly distributed on [0, 6].

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Given a normal distribution with mean -10 and standard deviation 5, find the area under the normal curve and above the
given interval on the horizontal axis.
-

Accepted Answer

A)  0.0228 
B)  0.1815 
C)  0.1587 
D)  0.1359 
A)  0.0228 
B)  0.1815 
C)  0.1587 
D)  0.1359

Solve the problem. -

Solve the problem. -The shelf life (in days) of a perishable drug is a continuous random variable with probability density function f(x) as shown below. Find the median shelf life.

Find the value of the improper integral that converges. -

Find the probability density function f and the associated cumulative distribution function F for the continuous random variable X if -X is uniformly distributed on [1, 7].

X is a continuous random variable with mean µ and standard deviation σ. Find µ and σ, and then find P(µ -σ ≤ X ≤ µ +σ) if -X is uniformly distributed on [-6, 6].

Find the median for f(x). -

Find the associated cumulative distribution function. Graph both functions (on separate sets of axes). -

Find a constant k so that kf is a probability density function, or state it does not exist. -

Find the value of the improper integral that converges. -

Solve the problem. -Find the area under the standard normal curve and above the given interval on the horizontal axis.

Find the mean, median, and standard deviation of the continuous random variable X if -X is an exponential random variable with λ = 2.

Solve the problem. -The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function f(x) as shown below. Find the median waiting time. Round to three decimal places.

The quartile points for a probability density function are the values that divide the area under the graph of the function into four equal parts. Find the quartile points for the probability density function f(x). -

F(x) is the cumulative distribution function for a continuous random variable X. Find the probability density function f(x) associated with F(x). -

Solve the problem. -

X is a continuous random variable with mean and then find ) if -X is uniformly distributed on [0, 6].

Given a normal distribution with mean -10 and standard deviation 5, find the area under the normal curve and above the given interval on the horizontal axis. -

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Basic Algebra Review

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Exam 11: Probability and Calculus

Solve the problem. -

Solve the problem. -The shelf life (in days) of a perishable drug is a continuous random variable with probability density function f(x) as shown below. Find the median shelf life.

Find the value of the improper integral that converges. -

Find the probability density function f and the associated cumulative distribution function F for the continuous random variable X if -X is uniformly distributed on [1, 7].

X is a continuous random variable with mean µ and standard deviation σ. Find µ and σ, and then find P(µ -σ ≤ X ≤ µ +σ) if -X is uniformly distributed on [-6, 6].

Find the median for f(x). -

Find the associated cumulative distribution function. Graph both functions (on separate sets of axes). -

Find a constant k so that kf is a probability density function, or state it does not exist. -

Find the value of the improper integral that converges. -

Solve the problem. -Find the area under the standard normal curve and above the given interval on the horizontal axis.

Find the mean, median, and standard deviation of the continuous random variable X if -X is an exponential random variable with λ = 2.

Solve the problem. -The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function f(x) as shown below. Find the median waiting time. Round to three decimal places.

The quartile points for a probability density function are the values that divide the area under the graph of the function into four equal parts. Find the quartile points for the probability density function f(x). -

F(x) is the cumulative distribution function for a continuous random variable X. Find the probability density function f(x) associated with F(x). -

Solve the problem. -

X is a continuous random variable with mean and then find ) if -X is uniformly distributed on [0, 6].

Given a normal distribution with mean -10 and standard deviation 5, find the area under the normal curve and above the given interval on the horizontal axis. -

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Basic Algebra Review

Special Topics

Filters