Question 1

List the four requirements for a binomial distribution. Describe an experiment which is binomial and discuss how the experiment fits each of the four requirements.

Accepted Answer

The four requirements are: 1)The experim

Question 2

Find the mean of the binomial random variable. Round to two decimal places when necessary.
-According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size

Accepted Answer

A) 16. 4 
B) 2.75 
C) 3.52 
D) 0.22 
A) 16. 4 
B) 2.75 
C) 3.52 
D) 0.22

Question 3

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise.
-A contractor is considering a sale that promises a profit of $27,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such)of $2000 with a probability of 0.3. What is the expected
Profit? Round the answer to the nearest dollar.

Accepted Answer

A) $18,300 
B) $20,300 
C) $25,000 
D) $18,900 
A) $18,300 
B) $20,300 
C) $25,000 
D) $18,900

Question 4

Let the random variable X represent the winnings at one play of a particular game. The expected value of X is known to be -$0.32. This means that on any given play of the game, the most likely outcome is that the player will lose 32 cents?

Accepted Answer

A) True 
 B)False

Question 5

Use random-variable notation to represent the event.
-Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. Use random-variable notation to represent the event that the product of the two numbers is greater
Than 4.

Accepted Answer

A)  $\{ X Y > 4 \}$ 
B)  $\{ 5,6 \}$ 
C)  $\mathrm { P } \{ \mathrm { Y } > 4 \}$ 
D)  $\{ Y > 4 \}$ 
A)  $\{ X Y > 4 \}$ 
B)  $\{ 5,6 \}$ 
C)  $\mathrm { P } \{ \mathrm { Y } > 4 \}$ 
D)  $\{ Y > 4 \}$

Question 6

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise.
-Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?

Accepted Answer

A) -$1.00 
B) -$0.40 
C) -$0.50 
D) $0.00 
A) -$1.00 
B) -$0.40 
C) -$0.50 
D) $0.00

Question 7

Determine the possible values of the random variable.
-The following frequency distribution lists the annual household incomes (in thousands of dollars) of one neighborhood in a large city. For a randomly selected income between $200,000 and $700,000, let Y denote the number of households with that income. What are the possible values of The random variable Y? 
$\begin{array}{c|c}
\text { Incomes } & \text { Frequency } \
\hline 200-300 & 69 \
301-400 & 62 \
401-500 & 75 \
501-600 & 78 \
601-700 & 18
\end{array}$

Accepted Answer

A) $69,62,75,78,18$ 
B)  18 
C)  302 
D)  $69,62,75,78$ 
A) $69,62,75,78,18$ 
B)  18 
C)  302 
D)  $69,62,75,78$

Question 8

Find the indicated probability. Round to four decimal places.
-The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 10 participants there have been
Only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer Women when 10 people are picked?

Accepted Answer

A) 0.0547 
B) 0.0439 
C) 0.0107 
D) 0.0537 
A) 0.0547 
B) 0.0439 
C) 0.0107 
D) 0.0537

Question 9

Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places.
-The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson approximation to the binomial distribution to find the probability that among 11,000
Cars passing through this tunnel, at least one will have a flat tire.

Accepted Answer

A) 0.513 
B) 0.356 
C) 0.644 
D) 0.283 
A) 0.513 
B) 0.356 
C) 0.644 
D) 0.283

Question 10

Find the standard deviation of the random variable.
-The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table. Round
The answer to two decimal places. $\begin{array}{c|ccccc}
\mathrm{x} & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.0081 & 0.0756 & 0.2646 & 0.4116 & 0.2401
\end{array}$

Accepted Answer

A) $2.95$ 
B)  $1.06$ 
C)  $0.92$ 
D)  $0.84$ 
A) $2.95$ 
B)  $1.06$ 
C)  $0.92$ 
D)  $0.84$

Question 11

Find the specified probability.
-Use the special addition rule and the following probability distribution to determine $\mathrm { P } ( 6 < X \leq 8 )$.
$\begin{array}{cccccccc}
\mathrm{X} & 5 & 6 & 7 & 8 & 9 & 10 & 11 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.05 & 0.05 & 0.20 & 0.15 & 0.15 & 0.10 & 0.30
\end{array}$

Accepted Answer

A) $1.00$ 
B)  $0.35$ 
C)  $0.40$ 
D)  $0.45$ 
A) $1.00$ 
B)  $0.35$ 
C)  $0.40$ 
D)  $0.45$

Question 12

Find the mean of the binomial random variable. Round to two decimal places when necessary.
-The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 12. Find the mean for the random variable X, the number of seeds germinating in each batch.

Accepted Answer

A) 10.8 
B) 3.6 
C) 8.52 
D) 8.4 
A) 10.8 
B) 3.6 
C) 8.52 
D) 8.4

Question 13

Provide an appropriate response.
-A die is rolled repeatedly until a six appears. The random variable X represents the total number of rolls preceding the six. What are the possible values of the random variable X?

Accepted Answer

A) 0, 1, 2, 3, 4, ..... 
B) 0, 1, 2, 3, 4, 5, 6 
C) 1, 2, 3, 4, ..... 
D) 1, 2, 3, 4, 5, 6 
A) 0, 1, 2, 3, 4, ..... 
B) 0, 1, 2, 3, 4, 5, 6 
C) 1, 2, 3, 4, ..... 
D) 1, 2, 3, 4, 5, 6

Question 14

Find the indicated binomial probability. Round to five decimal places when necessary.
-A company manufactures calculators in batches of 64 and there is a 4% rate of defects. Find the probability of getting exactly 4 defects in a batch.

Accepted Answer

A) 1.62656 
B) 54,866.1882 
C) 3.84 
D) 0.14046 
A) 1.62656 
B) 54,866.1882 
C) 3.84 
D) 0.14046

Question 15

What is the probability that 6 rolls of a fair die will show four exactly 2 times?

Accepted Answer

A) 0.0134 
B) 0.0067 
C) 0.41667 
D) 0.20094 
A) 0.0134 
B) 0.0067 
C) 0.41667 
D) 0.20094

Question 16

Find the mean of the binomial random variable. Round to two decimal places when necessary.
-The probability is 0.3 that a person shopping at a certain store will spend less than $20. For groups of size 16, find the mean number who spend less than $20.

Accepted Answer

A) 14 
B) 11.2 
C) 6 
D) 4.8 
A) 14 
B) 11.2 
C) 6 
D) 4.8

Question 17

Find the mean of the Poisson random variable.
-Suppose $X$ has a Poisson distribution with parameter $\lambda = 1.4$. Find the mean of $X$.

Accepted Answer

A) $1.4$ 
B)  $1.183$ 
C)  1 
D)  $1.96$ 
A) $1.4$ 
B)  $1.183$ 
C)  1 
D)  $1.96$

Question 18

Obtain the probability distribution of the random variable.
-The following table displays a frequency distribution for the number of living grandparents for students at a high school. For a randomly selected student in the school, let X denote the number of Living grandparents of the student. Obtain the probability distribution of X. $\begin{array}{r|rrrrr}
\text { Number of living grandparents } & 0 & 1 & 2 & 3 & 4 \
\hline \text { Frequency } & 38 & 85 & 157 & 216 & 154
\end{array}$

Accepted Answer

A) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.066 \
1 & 0.146 \
2 & 0.242 \
3 & 0.317 \
4 & 0.229
\end{array}$ 
B) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.2 \
1 & 0.2 \
2 & 0.2 \
3 & 0.2 \
4 & 0.2
\end{array}$ 
C) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 1 & 0.139 \
2 & 0.257 \
3 & 0.353 \
4 & 0.252
\end{array}$ 
D) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.058 \
1 & 0.131 \
2 & 0.242 \
3 & 0.332 \
4 & 0.237
\end{array}$ 
A) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.066 \
1 & 0.146 \
2 & 0.242 \
3 & 0.317 \
4 & 0.229
\end{array}$ 
B) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.2 \
1 & 0.2 \
2 & 0.2 \
3 & 0.2 \
4 & 0.2
\end{array}$ 
C) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 1 & 0.139 \
2 & 0.257 \
3 & 0.353 \
4 & 0.252
\end{array}$ 
D) 
$\begin{array}{r|r}
\text { Grandparents } & \text { Probability } \
\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \
\hline 0 & 0.058 \
1 & 0.131 \
2 & 0.242 \
3 & 0.332 \
4 & 0.237
\end{array}$

Question 19

Use random-variable notation to represent the event.
-The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let Y denote the number of siblings of
The student. $\begin{array}{r|rrrrrrrr}
\text { Number of siblings } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Frequency } & 189 & 245 & 102 & 42 & 24 & 13 & 5 & 2
\end{array}$

Use random-variable notation to represent the event that the student obtained has at least two but fewer than six siblings.

Accepted Answer

A) $\{ 2 \leq Y \leq 6 \}$ 
B)  $\{ 2,3,4,5 \}$ 
C)  $\{ 2 < Y < 6 \}$ 
D)  $\{ 2 \leq Y < 6 \}$ 
A) $\{ 2 \leq Y \leq 6 \}$ 
B)  $\{ 2,3,4,5 \}$ 
C)  $\{ 2 < Y < 6 \}$ 
D)  $\{ 2 \leq Y < 6 \}$

Question 20

Find the mean of the random variable.
-The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table. Round
The answer to two decimal places. $\begin{array}{c|ccccc}
\mathrm{X} & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.1296 & 0.3456 & 0.3456 & 0.1536 & 0.0256
\end{array}$

Accepted Answer

A) $1.50$ 
B)  $1.73$ 
C)  $2.00$ 
D)  $1.60$ 
A) $1.50$ 
B)  $1.73$ 
C)  $2.00$ 
D)  $1.60$

List the four requirements for a binomial distribution. Describe an experiment which is binomial and discuss how the experiment fits each of the four requirements.

Find the mean of the binomial random variable. Round to two decimal places when necessary. -According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size

Let the random variable X represent the winnings at one play of a particular game. The expected value of X is known to be -$0.32. This means that on any given play of the game, the most likely outcome is that the player will lose 32 cents?

Use random-variable notation to represent the event. -Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. Use random-variable notation to represent the event that the product of the two numbers is greater Than 4.

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise. -Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?

Find the specified probability. -Use the special addition rule and the following probability distribution to determine $\mathrm { P } ( 6 < X \leq 8 )$ . 5 6 7 8 9 10 11 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

Find the mean of the binomial random variable. Round to two decimal places when necessary. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 12. Find the mean for the random variable X, the number of seeds germinating in each batch.

Provide an appropriate response. -A die is rolled repeatedly until a six appears. The random variable X represents the total number of rolls preceding the six. What are the possible values of the random variable X?

Find the indicated binomial probability. Round to five decimal places when necessary. -A company manufactures calculators in batches of 64 and there is a 4% rate of defects. Find the probability of getting exactly 4 defects in a batch.

What is the probability that 6 rolls of a fair die will show four exactly 2 times?

Find the mean of the binomial random variable. Round to two decimal places when necessary. -The probability is 0.3 that a person shopping at a certain store will spend less than $20. For groups of size 16, find the mean number who spend less than $20.

Find the mean of the Poisson random variable. -Suppose $X$ has a Poisson distribution with parameter $\lambda = 1.4$ . Find the mean of $X$ .

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

List the four requirements for a binomial distribution. Describe an experiment which is binomial and discuss how the experiment fits each of the four requirements.

Find the mean of the binomial random variable. Round to two decimal places when necessary. -According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size

Let the random variable X represent the winnings at one play of a particular game. The expected value of X is known to be -$0.32. This means that on any given play of the game, the most likely outcome is that the player will lose 32 cents?

Use random-variable notation to represent the event. -Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. Use random-variable notation to represent the event that the product of the two numbers is greater Than 4.

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise. -Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?

Find the specified probability. -Use the special addition rule and the following probability distribution to determine P(6<X≤8)\mathrm { P } ( 6 < X \leq 8 )P(6<X≤8) . 5 6 7 8 9 10 11 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

Find the mean of the binomial random variable. Round to two decimal places when necessary. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 12. Find the mean for the random variable X, the number of seeds germinating in each batch.

Provide an appropriate response. -A die is rolled repeatedly until a six appears. The random variable X represents the total number of rolls preceding the six. What are the possible values of the random variable X?

Find the indicated binomial probability. Round to five decimal places when necessary. -A company manufactures calculators in batches of 64 and there is a 4% rate of defects. Find the probability of getting exactly 4 defects in a batch.

What is the probability that 6 rolls of a fair die will show four exactly 2 times?

Find the mean of the binomial random variable. Round to two decimal places when necessary. -The probability is 0.3 that a person shopping at a certain store will spend less than $20. For groups of size 16, find the mean number who spend less than $20.

Find the mean of the Poisson random variable. -Suppose XXX has a Poisson distribution with parameter λ=1.4\lambda = 1.4λ=1.4 . Find the mean of XXX .

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

Find the specified probability. -Use the special addition rule and the following probability distribution to determine $\mathrm { P } ( 6 < X \leq 8 )$ . 5 6 7 8 9 10 11 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

Find the mean of the Poisson random variable. -Suppose $X$ has a Poisson distribution with parameter $\lambda = 1.4$ . Find the mean of $X$ .