Question 1

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.

Accepted Answer

A)  $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \
\end{array}$ 
B)    $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$ 
C)    $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \
\end{array}$ 
D)    $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$ 
E)    $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\end{array}$ 
A)  $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \
\end{array}$ 
B)    $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$ 
C)    $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \
\end{array}$ 
D)    $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$ 
E)    $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\end{array}$

Question 2

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline x & - 20 & - 13 & 1 & 13 & 20 & 25 \
\hline P ( X = x ) & 0.1 & 0.1 & 0.1 & 0.2 & 0 & 0.5 \
\hline
\end{array}$$   Round your answer to two decimal places if necessary.

Accepted Answer

A) 261.69 
B)  162.19 
C)  1,757.64 
D)  11.9 
E)  16.18 
A) 261.69 
B)  162.19 
C)  1,757.64 
D)  11.9 
E)  16.18

Question 3

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. P - the energy of an electron in a hydrogen atom. ​
Classify the random variable P as finite, discrete infinite, or continuous.
​

Accepted Answer

A) P is a finite random variable. 
B)  P is a discrete infinite random variable. 
C)  P is a continuous random variable. 
A) P is a finite random variable. 
B)  P is a discrete infinite random variable. 
C)  P is a continuous random variable.

Question 4

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age  Round your answer to four decimal places. ?

Accepted Answer

A) 0.3333 
B)  0.784 
C)  0.6 
D)  0.216 
E)  0.0556 
A) 0.3333 
B)  0.784 
C)  0.6 
D)  0.216 
E)  0.0556

Question 5

Let X be the number of heads that come up when a coin is tossed twice. Calculate the expected value of the given random variable X.
​ $E ( X ) =$ __________

Accepted Answer

The answer of Let X be the number of heads...

Question 6

The table shows crashworthiness ratings for several categories of motor vehicles. Take X as the crash-test rating of a small car,  Y as the crash-test rating for a small SUV, and so on, as shown in the table.   $$\begin{array} { | l | l | l | l | l | l | l | } \hline&&\text { Overall Frontal Crash Test Rating }\
\hline & \begin{array} { l } 
\text { Number } \
\text { Tested }
\end{array} & \begin{array} { l } 
\text { 3 } \
( \text { Good) }
\end{array} & \begin{array} { l } 
\text { 2 } \
\text { (Acceptable) }
\end{array} & \begin{array} { l } 1\
\text { (Marginal) } \
\end{array}& \begin{array} { l } 0\
\text { (poor) } \
\end{array} \
\hline \text { Small Cars } X & 16 & 1 & 11 & 2 & 2 \
\hline \text { Small SUVs } Y & 10 & 1 & 4 & 4 & 1 \
\hline \text { Medium SUVs } Z & 13 & 2 & 5 & 2 & 4 \
\hline \text { Passenger Vans } U & 11 & 2 & 0 & 2 & 7 \
\hline \text { Midsize Cars } V & 14 & 2 & 5 & 0 & 7 \
\hline \text { Large Cars } W & 19 & 9 & 5 & 3 & 2 \
\hline
\end{array}$$  
Compute the probability distribution for X.

Accepted Answer

A)   $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.1&0.6875&0.10625&0.10625 \
\end{array}$ 
B)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.125&0.0625&0.6875&0.125 \
\end{array}$ 
C)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.0625&0.6875&0.125&0.125 \
\end{array}$ 
D)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.125&0.125&0.6875&0.0625 \
\end{array}$ 
E)  $\begin{array} { l  }
x&3&2&1&0\P(X=x)&0.10625&0.1&0.6875&0.10625
\end{array}$ 
A)   $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.1&0.6875&0.10625&0.10625 \
\end{array}$ 
B)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.125&0.0625&0.6875&0.125 \
\end{array}$ 
C)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.0625&0.6875&0.125&0.125 \
\end{array}$ 
D)  $\begin{array} { l } 
x & 3&2&1&0\
P ( X = x ) &0.125&0.125&0.6875&0.0625 \
\end{array}$ 
E)  $\begin{array} { l  }
x&3&2&1&0\P(X=x)&0.10625&0.1&0.6875&0.10625
\end{array}$

Question 7

The following is a sample of tow ratings (in pounds) for some popular 2000 model sport utility vehicles.  
6,400, 12,800, 19,200, 25,600, 32,000, 38,400
 
Compute the median.

Accepted Answer

A)  $m = 22,400$ 
B)  $m = 9,600$ 
C)  $m = 38,400$ 
D)  $m = 19,200$ 
E)  $m = 5,850$ 
A)  $m = 22,400$ 
B)  $m = 9,600$ 
C)  $m = 38,400$ 
D)  $m = 19,200$ 
E)  $m = 5,850$

Question 8

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 7 participants, what is the probability that an investigator will draw at least 1 female  Please round your answer to four decimal places.

Accepted Answer

The answer of In a large on-the-job training program, half...

Question 9

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Accepted Answer

The answer of LSAT test scores are normally distributed with...

Question 10

Calculate the expected value of X for the given probability distribution. $$\begin{array} { c c c c c } 
x & 1 & 2 & 3 & 4 \
P ( X = x ) & 0.4 & 0.2 & 0.2 & 0.2
\end{array}$$ ​ $$E ( X ) =$$ __________

Accepted Answer

The answer of Calculate the expected value of X for...

Question 11

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

Accepted Answer

The answer of Find the probability that a normal variable...

Question 12

The following table shows the approximate number of males of Hispanic origin employed in the U.S., broken down by age group. $$\begin{array} { | c | c | c | c | } 
\hline \text { Age } & 15 - 24.9 & 25 - 54.9 & 55 - 64.9 \
\hline \begin{array} { c } 
\text { Employment } \
\text { (thousands) }
\end{array} & 17,000 & 13,000 & 1,500 \
\hline
\end{array}$$  
Use the rounded midpoints of the given measurement classes to compute the expected value and the standard deviation of the age X of a male Hispanic worker in the U.S. Please round your answers to two decimal places. $\mu =$ __________ $\sigma =$ __________
In what age interval does the empirical rule predict that 68 percent of all male Hispanic workers will fall  Please round answers to the nearest year.
from __________ to __________

Accepted Answer

30.16; 11.

Question 13

You are performing 5 independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.

Accepted Answer

A) 0.9421 
B)  0.9997 
C)  0.0579 
D)  0.9933 
E)  0.0410 
A) 0.9421 
B)  0.9997 
C)  0.0579 
D)  0.9933 
E)  0.0410

Question 14

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places. ​

Accepted Answer

A) 0.5907 
B)  0.8185 
C)  0.2954 
D)  0.1815 
E)  0.8175 
A) 0.5907 
B)  0.8185 
C)  0.2954 
D)  0.1815 
E)  0.8175

Question 15

Calculate the expected value, the variance, and the standard deviation of the given random variable X.
​
Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.3. Let X be the number of bull's-eyes hit.
​
Please round your answers to two decimal places, if necessary.
​ $\mu = E ( X ) =$ __________
​ $\sigma ^ { 2 } =$ __________
​ $\sigma =$ __________

Accepted Answer

The answer of Calculate the expected value, the variance, and...

Question 16

According to quantum mechanics, the energy of an electron in a hydrogen atom can assume only the values $\frac { s } { 1 }$ , $\frac { s } { 4 }$ , $\frac { s } { 9 }$ , $\frac { s } { 16 }$ ... for a certain constant value s. X - the energy of an electron in a hydrogen atom.
​
Classify the random variable ​X as finite, discrete infinite, or continuous.

Accepted Answer

The answer of According to quantum mechanics, the energy of...

Question 17

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline P ( X = x ) & 0.05 & 0.11 & 0.34 & 0.24 & 0.14 & 0.06 & 0.02 & 0.02 & 0.01 & 0.01 \
\hline
\end{array}$$ ​
Compute the mean. Please round your answer to one decimal place. $\mu =$ __________
Compute the variance. Use the rounded value for the mean in your calculations. Round your answer to one decimal place. $\sigma ^ { 2 } =$ __________
Compute the standard deviation. Use the rounded value for the variance in your calculations. Round your answer to one decimal place. $\sigma =$ __________
As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75 percent of all cities. Find this range. Please round your answers to one decimal place.
from __________ to __________
Find the largest number of video arcades you should install so as to comply with this regulation.
The largest number is __________.

Accepted Answer

2.8; 2.7;

Question 18

Let X be the number of tails that come up when a coin is tossed three times. Calculate the expected value of the given random variable X.

Accepted Answer

A)  $E ( X ) = 2$ 
B)  $E ( X ) = 3$ 
C)  $E ( X ) = 6$ 
D)  $E ( X ) = 1.5$ 
E)  $E ( X ) = 2.25$ 
A)  $E ( X ) = 2$ 
B)  $E ( X ) = 3$ 
C)  $E ( X ) = 6$ 
D)  $E ( X ) = 1.5$ 
E)  $E ( X ) = 2.25$

Question 19

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising  (Assume that the times between failures are normally distributed.)

Accepted Answer

Since the time betwe

Question 20

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 90 crashes. Round your answer to four decimal places. Round Z to two decimal places. ​

Accepted Answer

A) 0.5332 
B)  0.7804 
C)  0.7784 
D)  0.5342 
E)  0.7794 
A) 0.5332 
B)  0.7804 
C)  0.7784 
D)  0.5342 
E)  0.7794

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.

Calculate the standard deviation of X for the probability distribution. x -20 -13 1 13 20 25 P(X=x) 0.1 0.1 0.1 0.2 0 0.5 Round your answer to two decimal places if necessary.

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. P - the energy of an electron in a hydrogen atom. Classify the random variable P as finite, discrete infinite, or continuous.

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age Round your answer to four decimal places. ?

Let X be the number of heads that come up when a coin is tossed twice. Calculate the expected value of the given random variable X. $E ( X ) =$ __________

The following is a sample of tow ratings (in pounds) for some popular 2000 model sport utility vehicles. 6,400, 12,800, 19,200, 25,600, 32,000, 38,400 Compute the median.

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 7 participants, what is the probability that an investigator will draw at least 1 female Please round your answer to four decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.4 0.2 0.2 0.2 $E ( X ) =$ __________

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

You are performing 5 independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places.

Let X be the number of tails that come up when a coin is tossed three times. Calculate the expected value of the given random variable X.

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 90 crashes. Round your answer to four decimal places. Round Z to two decimal places.

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

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Exam 9: Random Variables and Statistics

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.

Calculate the standard deviation of X for the probability distribution. x -20 -13 1 13 20 25 P(X=x) 0.1 0.1 0.1 0.2 0 0.5 Round your answer to two decimal places if necessary.

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. P - the energy of an electron in a hydrogen atom. ​ Classify the random variable P as finite, discrete infinite, or continuous. ​

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age Round your answer to four decimal places. ?

Let X be the number of heads that come up when a coin is tossed twice. Calculate the expected value of the given random variable X. ​ E(X)=E ( X ) =E(X)= __________

The following is a sample of tow ratings (in pounds) for some popular 2000 model sport utility vehicles. 6,400, 12,800, 19,200, 25,600, 32,000, 38,400 Compute the median.

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 7 participants, what is the probability that an investigator will draw at least 1 female Please round your answer to four decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.4 0.2 0.2 0.2 ​ E(X)=E ( X ) =E(X)= __________

Find the probability that a normal variable takes values more than 14\frac { 1 } { 4 }41​ standard deviations away from its mean. Please, round the answer to three decimal places.

You are performing 5 independent Bernoulli trials with p=0.8p = 0.8p=0.8 and q=0.2q = 0.2q=0.2 . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places. ​

Let X be the number of tails that come up when a coin is tossed three times. Calculate the expected value of the given random variable X.

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 90 crashes. Round your answer to four decimal places. Round Z to two decimal places. ​

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. P - the energy of an electron in a hydrogen atom. Classify the random variable P as finite, discrete infinite, or continuous.

Let X be the number of heads that come up when a coin is tossed twice. Calculate the expected value of the given random variable X. $E ( X ) =$ __________

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.4 0.2 0.2 0.2 $E ( X ) =$ __________

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

You are performing 5 independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places.

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 90 crashes. Round your answer to four decimal places. Round Z to two decimal places.