Question 1

Find the expected value $E ( x )$ for the following probability distribution. Round your answer to three decimal places. $x$ $-$ 5,000 $-$ 2,500 300 $P ( x )$ 0.012
0.052
0.936

Accepted Answer

A) 9.529 
B) 837.255 
C) 8,244.640 
D) 700,995.360 
E) 90.800 
A) 9.529 
B) 837.255 
C) 8,244.640 
D) 700,995.360 
E) 90.800

Question 2

A computer manufacturer offers a computer system with three different disk drives, two different monitors, and five different keyboards. How many different computer systems could a consumer purchase from this manufacturer?

Accepted Answer

A) 16 
B) 24 
C) 30 
D) 20 
E) 60 
A) 16 
B) 24 
C) 30 
D) 20 
E) 60

Question 3

Determine whether the table represents a probability distribution. $$\begin{array} { | l | l | l | l | l | } 
\hline x & 0 & 1 & 2 & 3 \
\hline P ( x ) & 0.10 & 0.45 & 0.30 & 0.15 \
\hline
\end{array}$$

Accepted Answer

A) yes 
B) no 
A) yes 
B) no

Question 4

Calculate the binomial coefficient: $7 C _ { 5 }$

Accepted Answer

A) 2520 
B) 35 
C) 21 
D) 1 
E) 0 
A) 2520 
B) 35 
C) 21 
D) 1 
E) 0

Question 5

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 $f ( t ) = \frac { 5 } { 324 } t \sqrt { 9 - t }$ over the interval $[ 0,9 ]$ . Find the probability that a new employee will learn to operate the machine in more than 3 hours but less than 7 hours.

Accepted Answer

A) 0.6634 
B) 0.3052 
C) 0.5895 
D) 0.2733 
E) 0.4632 
A) 0.6634 
B) 0.3052 
C) 0.5895 
D) 0.2733 
E) 0.4632

Question 6

Find $P ( x \leq 3 )$ given the probability distribution. $$\begin{array} { l l l l l l l } 
x & 0 & 1 & 2 & 3 & 4 & 5 \
P ( x ) & 0.045 & 0.181 & 0.248 & 0.328 & 0.154 & 0.044
\end{array}$$

Accepted Answer

A) 0.328 
B) 0.474 
C) 0.526 
D) 0.802 
E) 0.198 
A) 0.328 
B) 0.474 
C) 0.526 
D) 0.802 
E) 0.198

Question 7

Find Pk+1 for the given Pk. $P _ { k } = \frac { 6 } { k ( k + 1 ) }$

Accepted Answer

A)  $P _ { k + 1 } = \frac { 6 } { k ( k + 1 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 6 } { k ( k + 1 ) } + \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $P _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $P _ { k + 1 } = \frac { 6 } { k ( k + 2 ) }$ 
E)  $P _ { k + 1 } = \frac { 36 } { ( k + 1 ) ( k + 2 ) }$ 
A)  $P _ { k + 1 } = \frac { 6 } { k ( k + 1 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 6 } { k ( k + 1 ) } + \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $P _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $P _ { k + 1 } = \frac { 6 } { k ( k + 2 ) }$ 
E)  $P _ { k + 1 } = \frac { 36 } { ( k + 1 ) ( k + 2 ) }$

Question 8

In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used. How many distinct license plate numbers can be formed?

Accepted Answer

A) 57,600,000 
B) 5,760,000 
C) 13,824,000 
D) 138,240,000 
E) 331,776,000 
A) 57,600,000 
B) 5,760,000 
C) 13,824,000 
D) 138,240,000 
E) 331,776,000

Question 9

Evaluate the binomial coefficient. $\left( \begin{array} { l } 
9 \
6
\end{array} \right)$

Accepted Answer

A)  $504$ 
B)  $84$ 
C)  $362,880$ 
D)  $6$ 
E)  $720$ 
A)  $504$ 
B)  $84$ 
C)  $362,880$ 
D)  $6$ 
E)  $720$

Question 10

At a high school cafeteria, diners can choose one vegetable from a choice of 2 vegetables, one meat from a choice of 3 meats, one serving of bread from among 4 breads, and a dessert from among 4 desserts. How many meal configurations are possible?

Accepted Answer

A) 13 
B) 96 
C) 4 
D) 24 
E) 48 
A) 13 
B) 96 
C) 4 
D) 24 
E) 48

Question 11

The arrival time t of a bus at a bus stop is uniformly distributed between $08 : 00$ A.M. and $08 : 08$ A.M. What is the probability that you will miss the bus if you arrive at the bus stop at $08 : 02$ A.M.? Round your answer to two decimal places.

Accepted Answer

A) 0.25 
B) 0.67 
C) 0.36 
D) 0.33 
E) 0.57 
A) 0.25 
B) 0.67 
C) 0.36 
D) 0.33 
E) 0.57

Question 12

Find the mean, variance, and standard deviation of the uniform distribution $f ( x ) = \frac { 1 } { 18 }$ over the interval [0, 18] without using integration.

Accepted Answer

A)  $\begin{array} { l l } 
\text { expected value (mean) : } & 9.000 \
\text { variance: } & 27.000 \
\text { standard deviation: } & 5.196
\end{array}$ 
B)  $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 5.196
\end{array}$ 
C)  $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 9.000
\end{array}$ 
D)  $\begin{array} { l l } 
\text { expected value (mean) } : & 5.196 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 27.000
\end{array}$ 
E)  $\begin{array} { l l } 
\text { expected value (mean) } & 9.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 27.000
\end{array}$ 
A)  $\begin{array} { l l } 
\text { expected value (mean) : } & 9.000 \
\text { variance: } & 27.000 \
\text { standard deviation: } & 5.196
\end{array}$ 
B)  $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 5.196
\end{array}$ 
C)  $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 9.000
\end{array}$ 
D)  $\begin{array} { l l } 
\text { expected value (mean) } : & 5.196 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 27.000
\end{array}$ 
E)  $\begin{array} { l l } 
\text { expected value (mean) } & 9.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 27.000
\end{array}$

Question 13

A card is chosen at random from two 52-card decks of 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)  $\frac { 1 } { 13 }$ 
B)  $\frac { 3 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 3 } { 26 }$ 
E)  $\frac { 5 } { 26 }$ 
A)  $\frac { 1 } { 13 }$ 
B)  $\frac { 3 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 3 } { 26 }$ 
E)  $\frac { 5 } { 26 }$

Question 14

For the probability density function $f ( x ) = \frac { 7 } { 6 ( x + 1 ) ^ { 2 } }$ on the interval $[ 0,6 ]$ find the probability that $x \leq 4$ . Round your answer to the nearest hundredth.

Accepted Answer

A) 0.05 
B) 0.33 
C) 0.93 
D) 0.67 
E) 0.02 
A) 0.05 
B) 0.33 
C) 0.93 
D) 0.67 
E) 0.02

Question 15

For the given probability density function, find $\operatorname { Var } ( X )$ $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } \text { on } [ 0,2 ]$

Accepted Answer

A) 2.000 
B) 1.150 
C) 1.500 
D) 0.150 
E) 0.800 
A) 2.000 
B) 1.150 
C) 1.500 
D) 0.150 
E) 0.800

Question 16

You are given the probability that an event will not happen. Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = \frac { 3 } { 31 }$

Accepted Answer

A)  $\frac { 3 } { 31 }$ 
B) 0 
C) 1 
D)  $\frac { 28 } { 31 }$ 
E)  $\frac { 14 } { 31 }$ 
A)  $\frac { 3 } { 31 }$ 
B) 0 
C) 1 
D)  $\frac { 28 } { 31 }$ 
E)  $\frac { 14 } { 31 }$

Question 17

Use mathematical induction to prove the property for all positive integers n. $\left[ a ^ { n } \right] ^ { 2 } = a ^ { 2 n }$

Accepted Answer

1) n = 1: @#IMG-DLM& The statement is tr

Question 18

Find the median of the exponential probability density function $f ( t ) = \frac { 4 } { 5 } e ^ { - \frac { 4 t } { 5 } }$ over the interval $[ 0 , \infty )$ .

Accepted Answer

A) 0.555 
B) 0.693 
C) 0.866 
D) 0.485 
E) 0.400 
A) 0.555 
B) 0.693 
C) 0.866 
D) 0.485 
E) 0.400

Question 19

A publishing company introduces a new weekly magazine that sells for $4.95 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. $$\begin{array} { l l l l l l } 
x & 10 & 15 & 20 & 30 & 40 \
P ( x ) & 0.23 & 0.28 & 0.23 & 0.14 & 0.12
\end{array}$$

Accepted Answer

A)  $\$$ 99,495 
B)  $\$$ 99 
C)  $\$$ 455 
D)  $\$$ 20,100 
E)  $\$$ 455,351 
A)  $\$$ 99,495 
B)  $\$$ 99 
C)  $\$$ 455 
D)  $\$$ 20,100 
E)  $\$$ 455,351

Question 20

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 11 } \left( 8 n - 4 n ^ { 2 } \right)$

Accepted Answer

A) -1100 
B) -4488 
C) -396 
D) 264 
E) -1496 
A) -1100 
B) -4488 
C) -396 
D) 264 
E) -1496

Find the expected value $E ( x )$ for the following probability distribution. Round your answer to three decimal places. $x$ $-$ 5,000 $-$ 2,500 300 $P ( x )$ 0.012 0.052 0.936

A computer manufacturer offers a computer system with three different disk drives, two different monitors, and five different keyboards. How many different computer systems could a consumer purchase from this manufacturer?

Determine whether the table represents a probability distribution. x 0 1 2 3 P(x) 0.10 0.45 0.30 0.15

Calculate the binomial coefficient: $7 C _ { 5 }$

Find $P ( x \leq 3 )$ given the probability distribution. x 0 1 2 3 4 5 P(x) 0.045 0.181 0.248 0.328 0.154 0.044

Find Pk+1 for the given Pk. $P _ { k } = \frac { 6 } { k ( k + 1 ) }$

In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used. How many distinct license plate numbers can be formed?

Evaluate the binomial coefficient. $\left( \begin{array} { l } 9 \\6\end{array} \right)$

At a high school cafeteria, diners can choose one vegetable from a choice of 2 vegetables, one meat from a choice of 3 meats, one serving of bread from among 4 breads, and a dessert from among 4 desserts. How many meal configurations are possible?

The arrival time t of a bus at a bus stop is uniformly distributed between $08 : 00$ A.M. and $08 : 08$ A.M. What is the probability that you will miss the bus if you arrive at the bus stop at $08 : 02$ A.M.? Round your answer to two decimal places.

Find the mean, variance, and standard deviation of the uniform distribution $f ( x ) = \frac { 1 } { 18 }$ over the interval [0, 18] without using integration.

A card is chosen at random from two 52-card decks of 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 probability density function $f ( x ) = \frac { 7 } { 6 ( x + 1 ) ^ { 2 } }$ on the interval $[ 0,6 ]$ find the probability that $x \leq 4$ . Round your answer to the nearest hundredth.

For the given probability density function, find $\operatorname { Var } ( X )$ $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } \text { on } [ 0,2 ]$

You are given the probability that an event will not happen. Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = \frac { 3 } { 31 }$

Use mathematical induction to prove the property for all positive integers n. $\left[ a ^ { n } \right] ^ { 2 } = a ^ { 2 n }$

Find the median of the exponential probability density function $f ( t ) = \frac { 4 } { 5 } e ^ { - \frac { 4 t } { 5 } }$ over the interval $[ 0 , \infty )$ .

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 11 } \left( 8 n - 4 n ^ { 2 } \right)$

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Filters

Exam 17: Probability Web

Find the expected value E(x)E ( x )E(x) for the following probability distribution. Round your answer to three decimal places. xxx −-− 5,000 −-− 2,500 300 P(x)P ( x )P(x) 0.012 0.052 0.936

A computer manufacturer offers a computer system with three different disk drives, two different monitors, and five different keyboards. How many different computer systems could a consumer purchase from this manufacturer?

Determine whether the table represents a probability distribution. x 0 1 2 3 P(x) 0.10 0.45 0.30 0.15

Calculate the binomial coefficient: 7C57 C _ { 5 }7C5​

Find P(x≤3)P ( x \leq 3 )P(x≤3) given the probability distribution. x 0 1 2 3 4 5 P(x) 0.045 0.181 0.248 0.328 0.154 0.044

Find Pk+1 for the given Pk. Pk=6k(k+1)P _ { k } = \frac { 6 } { k ( k + 1 ) }Pk​=k(k+1)6​

In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used. How many distinct license plate numbers can be formed?

Evaluate the binomial coefficient. (96)\left( \begin{array} { l } 9 \\6\end{array} \right)(96​)

At a high school cafeteria, diners can choose one vegetable from a choice of 2 vegetables, one meat from a choice of 3 meats, one serving of bread from among 4 breads, and a dessert from among 4 desserts. How many meal configurations are possible?

The arrival time t of a bus at a bus stop is uniformly distributed between 08:0008 : 0008:00 A.M. and 08:0808 : 0808:08 A.M. What is the probability that you will miss the bus if you arrive at the bus stop at 08:0208 : 0208:02 A.M.? Round your answer to two decimal places.

Find the mean, variance, and standard deviation of the uniform distribution f(x)=118f ( x ) = \frac { 1 } { 18 }f(x)=181​ over the interval [0, 18] without using integration.

A card is chosen at random from two 52-card decks of 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 probability density function f(x)=76(x+1)2f ( x ) = \frac { 7 } { 6 ( x + 1 ) ^ { 2 } }f(x)=6(x+1)27​ on the interval [0,6][ 0,6 ][0,6] find the probability that x≤4x \leq 4x≤4 . Round your answer to the nearest hundredth.

For the given probability density function, find Var⁡(X)\operatorname { Var } ( X )Var(X) f(x)=38x2 on [0,2]f ( x ) = \frac { 3 } { 8 } x ^ { 2 } \text { on } [ 0,2 ]f(x)=83​x2 on [0,2]

You are given the probability that an event will not happen. Find the probability that the event will happen. P(E′)=331P \left( E ^ { \prime } \right) = \frac { 3 } { 31 }P(E′)=313​

Use mathematical induction to prove the property for all positive integers n. [an]2=a2n\left[ a ^ { n } \right] ^ { 2 } = a ^ { 2 n }[an]2=a2n

Find the median of the exponential probability density function f(t)=45e−4t5f ( t ) = \frac { 4 } { 5 } e ^ { - \frac { 4 t } { 5 } }f(t)=54​e−54t​ over the interval [0,∞)[ 0 , \infty )[0,∞) .

Find the sum using the formulas for the sums of powers of integers. ∑n=111(8n−4n2)\sum _ { n = 1 } ^ { 11 } \left( 8 n - 4 n ^ { 2 } \right)∑n=111​(8n−4n2)

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Filters

Find the expected value $E ( x )$ for the following probability distribution. Round your answer to three decimal places. $x$ $-$ 5,000 $-$ 2,500 300 $P ( x )$ 0.012 0.052 0.936

Calculate the binomial coefficient: $7 C _ { 5 }$

Find $P ( x \leq 3 )$ given the probability distribution. x 0 1 2 3 4 5 P(x) 0.045 0.181 0.248 0.328 0.154 0.044

Find Pk+1 for the given Pk. $P _ { k } = \frac { 6 } { k ( k + 1 ) }$

Evaluate the binomial coefficient. $\left( \begin{array} { l } 9 \\6\end{array} \right)$

The arrival time t of a bus at a bus stop is uniformly distributed between $08 : 00$ A.M. and $08 : 08$ A.M. What is the probability that you will miss the bus if you arrive at the bus stop at $08 : 02$ A.M.? Round your answer to two decimal places.

Find the mean, variance, and standard deviation of the uniform distribution $f ( x ) = \frac { 1 } { 18 }$ over the interval [0, 18] without using integration.

For the probability density function $f ( x ) = \frac { 7 } { 6 ( x + 1 ) ^ { 2 } }$ on the interval $[ 0,6 ]$ find the probability that $x \leq 4$ . Round your answer to the nearest hundredth.

For the given probability density function, find $\operatorname { Var } ( X )$ $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } \text { on } [ 0,2 ]$

You are given the probability that an event will not happen. Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = \frac { 3 } { 31 }$

Use mathematical induction to prove the property for all positive integers n. $\left[ a ^ { n } \right] ^ { 2 } = a ^ { 2 n }$

Find the median of the exponential probability density function $f ( t ) = \frac { 4 } { 5 } e ^ { - \frac { 4 t } { 5 } }$ over the interval $[ 0 , \infty )$ .

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 11 } \left( 8 n - 4 n ^ { 2 } \right)$