Question 1

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$$

Accepted Answer

A) $0.006$ 
B)  $0.085$ 
C)  $0.068$ 
D)  $0.173$ 
A) $0.006$ 
B)  $0.085$ 
C)  $0.068$ 
D)  $0.173$ C

Question 2

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$$

Accepted Answer

A) $0.599$ 
B)  $0.185$ 
C)  $0.216$ 
D)  $0.815$ 
A) $0.599$ 
B)  $0.185$ 
C)  $0.216$ 
D)  $0.815$ D

Question 3

The probability distribution of a random variable is given along with its mean and standard deviation. Draw aprobability histogram for the random variable; locate the mean and show one, two, and three standard deviationintervals.
-$\begin{array}{r|rrrrr}
\mathrm{x} & 4 & 5 & 6 & 7 & 8 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.1 & 0.3 & 0.45 & 0.1 & 0.05
\end{array}$

$$\mu = 5.7 , \sigma = 0.95$$

Accepted Answer

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

Question 4

Provide an appropriate response.
-Which of the random variables described below is likely to have a Poisson distribution? - The random variable X is the number of accidents occurring during a ski season at a particular
Ski resort.-Fifty people are selected at random from among the skiers at a particular resort. The random Variable Y is the number among the fifty who have been involved in a ski accident during the past Ski season. -One ski resort allows both skiers and snowboarders. Fifty people are selected at random from the People waiting in line at one of the resort's chairlifts. The random variable Z is the number of Snowboarders among the fifty.

Accepted Answer

A) X, Y, and Z 
B) Y and Z 
C) X only 
D) X and Y 
A) X, Y, and Z 
B) Y and Z 
C) X only 
D) X and Y

Question 5

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-For a certain type of fabric, the average number of defects in each square foot of fabric is 0.2. Find the probability that a randomly selected square foot of the fabric will contain more than one defect.

Accepted Answer

A) 0.016 
B) 0.836 
C) 0.982 
D) 0.018 
A) 0.016 
B) 0.836 
C) 0.982 
D) 0.018

Question 6

Find the standard deviation of the binomial random variable.
-A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

Accepted Answer

A) 1.543 
B) 2.06 
C) 1.537 
D) 1.491 
A) 1.543 
B) 2.06 
C) 1.537 
D) 1.491

Question 7

Calculate the specified probability
-Suppose that $\mathrm { T }$ is a random variable. Given that $\mathrm { P } ( 3.5 \leq \mathrm { T } \leq 3.5 ) = 0.275$, and that $\mathrm { P } ( \mathrm { K } $ 3.5), find $\mathrm { P } ( \mathrm { K } < - 3.5 )$.

Accepted Answer

A) $0.3625$ 
B)  $0.275$ 
C)  $1.75$ 
D)  $0.725$ 
A) $0.3625$ 
B)  $0.275$ 
C)  $1.75$ 
D)  $0.725$

Question 8

The random variable X represents the number of thunderstorms occurring in a month in one city. Suppose that X has a Poisson distribution with parameter $\lambda$ = 3.2. Determine and interpret the mean of the random variable X.

Accepted Answer

The mean of @#LAT-DLM& is @#LAT-DLM&. In

Question 9

Find the mean of the Poisson random variable.
-In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 1.8$. Let $X$ denote the number of burglaries in the town in a randomly selected week. Find the mean of X.

Accepted Answer

A) $1.342$ 
B)  $0.9$ 
C)  $1.8$ 
D)  $3.24$ 
A) $1.342$ 
B)  $0.9$ 
C)  $1.8$ 
D)  $3.24$

Question 10

Find the specified probability distribution of the binomial random variable.
-In one city, the probability that a person will pass his or her driving test on the first attempt is 0.69. Four people are selected at random from among those taking their driving test for the first time. Determine the probability distribution of X, the number among the four who pass the test.

Accepted Answer

A) 
$\begin{array}{r|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.2745 \
3 & 0.4074 \
4 & 0.2267
\end{array}$ 
B) 
$\begin{array}{c|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.1830 \
3 & 0.4074 \
4 & 0.2267
\end{array}$ 
C) 
$\begin{array}{r|r}
\mathrm{x} & \mathrm{P}(X=\mathrm{X}) \
\hline 1 & 0.69 \
2 & 0.4761 \
3 & 0.3285 \
4 & 0.2267
\end{array}$ 
D) 
$\begin{array}{c|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.2745 \
3 & 0.4254 \
4 & 0.2087
\end{array}$ 
A) 
$\begin{array}{r|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.2745 \
3 & 0.4074 \
4 & 0.2267
\end{array}$ 
B) 
$\begin{array}{c|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.1830 \
3 & 0.4074 \
4 & 0.2267
\end{array}$ 
C) 
$\begin{array}{r|r}
\mathrm{x} & \mathrm{P}(X=\mathrm{X}) \
\hline 1 & 0.69 \
2 & 0.4761 \
3 & 0.3285 \
4 & 0.2267
\end{array}$ 
D) 
$\begin{array}{c|r}
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.0092 \
1 & 0.0822 \
2 & 0.2745 \
3 & 0.4254 \
4 & 0.2087
\end{array}$

Question 11

Find the standard deviation of the binomial random variable.
-On a multiple choice test with 10 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random
Variable X, the number of correct answers.

Accepted Answer

A) 1.299 
B) 1.342 
C) 1.369 
D) 1.273 
A) 1.299 
B) 1.342 
C) 1.369 
D) 1.273

Question 12

Find the standard deviation of the binomial random variable.
-The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 11. Find the standard deviation for the random variable X, the number of seeds germinating in each
Batch.

Accepted Answer

A) 1.52 
B) 1.502 
C) 1.432 
D) 1.449 
A) 1.52 
B) 1.502 
C) 1.432 
D) 1.449

Question 13

For a particular game at a casino, let the random variable X represent the winnings (payoff minus bet)for one play of the game. The expected value of the random variable X is -$0.87. How would you interpret this statement?

Accepted Answer

In the long run, the

Question 14

Determine the possible values of the random variable.
-The following frequency distribution analyzes the scores on a math test. For a randomly selected score between 40 and 99, let Y denote the number of students with that score on the test. What are The possible values of the random variable Y? 
$\begin{array}{cc}
\hline \text { Scores } & \begin{array}{c}
\text { Number of } \
\text { students }
\end{array} \
\hline 40-59 & 2 \
60-75 & 4 \
76-82 & 6 \
83-94 & 15 \
95-99 & 5
\end{array}$

Accepted Answer

A) $2,4,6,5$ 
B)  $2,4,6,15,5$ 
C)  $2,4,6,15$ 
D)  32 
A) $2,4,6,5$ 
B)  $2,4,6,15,5$ 
C)  $2,4,6,15$ 
D)  32

Question 15

Find the indicated probability. Round to four decimal places.
-In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to
An ethnic minority?

Accepted Answer

A) 0.0547 
B) 0.9130 
C) 0.9846 
D) 0.9815 
A) 0.0547 
B) 0.9130 
C) 0.9846 
D) 0.9815

Question 16

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )$

Accepted Answer

A) $0.174$ 
B)  $0.162$ 
C)  $0.504$ 
D)  $0.169$ 
A) $0.174$ 
B)  $0.162$ 
C)  $0.504$ 
D)  $0.169$

Question 17

Describe the Poisson distribution and give some example of a random variable with a Poisson distribution.

Accepted Answer

The Poisson distribution is a

Question 18

Calculate the specified probability
-Suppose that $A$ is a random variable. Also suppose that $P ( T > a ) = P ( T < - a ) = x$, and that $P ( 0 < T \leq$ a ) $= y$. Find $P ( - a \leq T \leq 0 )$ in terms of $x$ and $y$.

Accepted Answer

A) $y$ 
B)  $1 - 2 x - y$ 
C)  $1 - y$ 
D)  $1 - ( 2 x - y )$ 
A) $y$ 
B)  $1 - 2 x - y$ 
C)  $1 - y$ 
D)  $1 - ( 2 x - y )$

Question 19

Calculate the specified probability
-Suppose that $D$ is a random variable. Given that $P ( D > 1.4 ) = 0.95$, find $P ( D \leq 1.4 )$.

Accepted Answer

A) $0.95$ 
B)  $0.05$ 
C)  $0.025$ 
D)  0 
A) $0.95$ 
B)  $0.05$ 
C)  $0.025$ 
D)  0

Question 20

Find the indicated probability. Round to four decimal places.
-A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass
The test?

Accepted Answer

A) 0.9990 
B) 0.0010 
C) 0.0102 
D) 0.0107 
A) 0.9990 
B) 0.0010 
C) 0.0102 
D) 0.0107

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$

The probability distribution of a random variable is given along with its mean and standard deviation. Draw aprobability histogram for the random variable; locate the mean and show one, two, and three standard deviationintervals. - 4 5 6 7 8 (=) 0.1 0.3 0.45 0.1 0.05 $\mu = 5.7 , \sigma = 0.95$

Find the standard deviation of the binomial random variable. -A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

Calculate the specified probability -Suppose that $\mathrm { T }$ is a random variable. Given that $\mathrm { P } ( 3.5 \leq \mathrm { T } \leq 3.5 ) = 0.275$ , and that $\mathrm { P } ( \mathrm { K } < 3.5 ) = \mathrm { P } ( \mathrm { K } >$ 3.5), find $\mathrm { P } ( \mathrm { K } < - 3.5 )$ .

The random variable X represents the number of thunderstorms occurring in a month in one city. Suppose that X has a Poisson distribution with parameter $\lambda$ = 3.2. Determine and interpret the mean of the random variable X.

Find the mean of the Poisson random variable. -In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 1.8$ . Let $X$ denote the number of burglaries in the town in a randomly selected week. Find the mean of X.

Find the standard deviation of the binomial random variable. -On a multiple choice test with 10 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random Variable X, the number of correct answers.

Find the standard deviation of the binomial random variable. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 11. Find the standard deviation for the random variable X, the number of seeds germinating in each Batch.

For a particular game at a casino, let the random variable X represent the winnings (payoff minus bet)for one play of the game. The expected value of the random variable X is -$0.87. How would you interpret this statement?

Find the indicated probability. Round to four decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to An ethnic minority?

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )$

Describe the Poisson distribution and give some example of a random variable with a Poisson distribution.

Calculate the specified probability -Suppose that $A$ is a random variable. Also suppose that $P ( T > a ) = P ( T < - a ) = x$ , and that $P ( 0 < T \leq$ a ) $= y$ . Find $P ( - a \leq T \leq 0 )$ in terms of $x$ and $y$ .

Calculate the specified probability -Suppose that $D$ is a random variable. Given that $P ( D > 1.4 ) = 0.95$ , find $P ( D \leq 1.4 )$ .

Find the indicated probability. Round to four decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass The test?

The Nature of Statistics

Organizing Data

Descriptive Measures

Probability Concepts

The Normal Distribution

The Sampling Distribution of the Sample Mean

Confidence Intervals for One Population Mean

Hypothesis Tests for One Population Mean

Inferences for Two Population Means

Inferences for Population Standard Deviations

Inferences for Population Proportions

Chi-Square Procedures

Descriptive Methods in Regression and Correlation

Inferential Methods in Regression and Correlation

Analysis of Variance Anova

Filters

Exam 5: Discrete Random Variables

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - λ=0.466;P(X=2)\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )λ=0.466;P(X=2)

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - λ=3.1;P(X≥2)\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )λ=3.1;P(X≥2)

Find the standard deviation of the binomial random variable. -A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

The random variable X represents the number of thunderstorms occurring in a month in one city. Suppose that X has a Poisson distribution with parameter λ\lambdaλ = 3.2. Determine and interpret the mean of the random variable X.

Find the mean of the Poisson random variable. -In one town, the number of burglaries in a week has a Poisson distribution with parameter λ=1.8\lambda = 1.8λ=1.8 . Let XXX denote the number of burglaries in the town in a randomly selected week. Find the mean of X.

Find the standard deviation of the binomial random variable. -On a multiple choice test with 10 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random Variable X, the number of correct answers.

Find the standard deviation of the binomial random variable. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 11. Find the standard deviation for the random variable X, the number of seeds germinating in each Batch.

For a particular game at a casino, let the random variable X represent the winnings (payoff minus bet)for one play of the game. The expected value of the random variable X is -$0.87. How would you interpret this statement?

Find the indicated probability. Round to four decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to An ethnic minority?

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - λ=4.5;P(X<3)\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )λ=4.5;P(X<3)

Describe the Poisson distribution and give some example of a random variable with a Poisson distribution.

Calculate the specified probability -Suppose that DDD is a random variable. Given that P(D>1.4)=0.95P ( D > 1.4 ) = 0.95P(D>1.4)=0.95 , find P(D≤1.4)P ( D \leq 1.4 )P(D≤1.4) .

Find the indicated probability. Round to four decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass The test?

The Nature of Statistics

Organizing Data

Descriptive Measures

Probability Concepts

The Normal Distribution

The Sampling Distribution of the Sample Mean

Confidence Intervals for One Population Mean

Hypothesis Tests for One Population Mean

Inferences for Two Population Means

Inferences for Population Standard Deviations

Inferences for Population Proportions

Chi-Square Procedures

Descriptive Methods in Regression and Correlation

Inferential Methods in Regression and Correlation

Analysis of Variance Anova

Filters

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$

The random variable X represents the number of thunderstorms occurring in a month in one city. Suppose that X has a Poisson distribution with parameter $\lambda$ = 3.2. Determine and interpret the mean of the random variable X.

Find the mean of the Poisson random variable. -In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 1.8$ . Let $X$ denote the number of burglaries in the town in a randomly selected week. Find the mean of X.

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )$

Calculate the specified probability -Suppose that $D$ is a random variable. Given that $P ( D > 1.4 ) = 0.95$ , find $P ( D \leq 1.4 )$ .