Question 1

Answer the question.
-Choosing 5 people (without replacement)from a group of 59 people, of which 15 are women, keeping track of the number of men chosen.

Accepted Answer

A) Not binomial: there are too many trials. 
B) Not binomial: there are more than two outcomes for each trial. 
C) Procedure results in a binomial distribution. 
D) Not binomial: the trials are not independent. 
A) Not binomial: there are too many trials. 
B) Not binomial: there are more than two outcomes for each trial. 
C) Procedure results in a binomial distribution. 
D) Not binomial: the trials are not independent.

Question 2

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth
-$\mathrm { n } = 665 ; \mathrm { p } = .7$

Accepted Answer

A)  $\mu = 467.2$ 
B)  $\boldsymbol { \mu } = 465.5$ 
C)  $\mu = 466.8$ 
D)  $\mu = 464.0$ 
A)  $\mu = 467.2$ 
B)  $\boldsymbol { \mu } = 465.5$ 
C)  $\mu = 466.8$ 
D)  $\mu = 464.0$

Question 3

The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by A, B, and C. Let P A = p1, P B = p2, P C = p3. In n independent trials, the probability of x1 outcomes of type $$A , x _ { 2 }$$ outcomes of type B, and x3 outcomes of type C is given by $$\frac { \mathrm { n } ! } { \left( \mathrm { x } _ { 1 } \right) ! \left( \mathrm { x } _ { 2 } \right) ! \left( \mathrm { x } _ { 3 } \right) ! } \cdot \mathrm { p } _ { 1 } \mathrm { x } _ { 1 } \cdot \mathrm { p } _ { 2 } ^ { \mathrm { x } _ { 2 } } \cdot \mathrm { p } _ { 3 } ^ { \mathrm { x } _ { 3 } }$$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all equally likely. If 13 offspring are tested, find the probability of getting exactly 2 A's,4 B's,2 C's, and 5 D's by expanding the above expression so that it applies to four types of outcomes instead of only three.

Accepted Answer

A) 0.96656 
B) 0.03222 
C) 0.00805 
D) 0.00201 
A) 0.96656 
B) 0.03222 
C) 0.00805 
D) 0.00201

Question 4

Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 5

The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.9. Find the probability that in a randomly selected year, the number of lightning strikes is 2.

Accepted Answer

A) 0.2617 
B) 0.1539 
C) 0.0128 
D) 0.2001 
A) 0.2617 
B) 0.1539 
C) 0.0128 
D) 0.2001

Question 6

Solve the problem.
-The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Accepted Answer

A) 0.39 
B) 0.63 
C) 0.76 
D) 0.56 
A) 0.39 
B) 0.63 
C) 0.76 
D) 0.56

Question 7

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth
-$n = 20 ; p = 3 / 5$

Accepted Answer

A)  $\mu = 12.3$ 
B)  $\mu = 12.0$ 
C)  $\boldsymbol { \mu } = 11.5$ 
D)  $\boldsymbol { \mu } = 12.7$ 
A)  $\mu = 12.3$ 
B)  $\mu = 12.0$ 
C)  $\boldsymbol { \mu } = 11.5$ 
D)  $\boldsymbol { \mu } = 12.7$

Question 8

Provide an appropriate response.
-Describe the differences in the Poisson and the binomial distribution.

Accepted Answer

The Poisson computes probabilities for o

Question 9

Provide an appropriate response.
-Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Accepted Answer

Probability distributions measure what w

Question 10

Provide an appropriate response.
-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 11

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2?
-n = 94, p = 0.20

Accepted Answer

A) Minimum: 11.04; maximum: 26.56 
B) Minimum: 14.92; maximum: 22.68 
C) Minimum: 26.56; maximum: 11.04 
D) Minimum: -11.28; maximum: 48.88 
A) Minimum: 11.04; maximum: 26.56 
B) Minimum: 14.92; maximum: 22.68 
C) Minimum: 26.56; maximum: 11.04 
D) Minimum: -11.28; maximum: 48.88

Question 12

Assume that x is a random variable in a probability distribution with mean µ and standard deviation ?. Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 3, then increased by 5.

Accepted Answer

A)  $\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5$ 
B)  $\mu _ { \text {new } } = 3 \mu + 5$; $\sigma _ { \text {new } } = 3 \sigma$ 
C)  $\mu _ { \text {new } } = 5 \mu + 3 ; \sigma _ { \text {new } } = 5 \sigma$ 
D)  $\mu _ { \text {new } } = \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma$ 
A)  $\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5$ 
B)  $\mu _ { \text {new } } = 3 \mu + 5$; $\sigma _ { \text {new } } = 3 \sigma$ 
C)  $\mu _ { \text {new } } = 5 \mu + 3 ; \sigma _ { \text {new } } = 5 \sigma$ 
D)  $\mu _ { \text {new } } = \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma$

Question 13

Focus groups of 12 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group)who recognize the Yummy brand name is 9.4, and the standard deviation is 0.98. Would it be unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name?

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 14

Solve the problem.
-According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Accepted Answer

A) 4.00 
B) 3.52 
C) 2.75 
D) 0.22 
A) 4.00 
B) 3.52 
C) 2.75 
D) 0.22

Question 15

Solve the problem.
-The probability of winning a certain lottery is 1/56,728. For people who play 517 times, find the standard deviation for the number of wins.

Accepted Answer

A) 0.0955 
B) 0.1046 
C) 0.0091 
D) 2.1706 
A) 0.0955 
B) 0.1046 
C) 0.0091 
D) 2.1706

Question 16

Solve the problem.
-The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 13. Find the standard deviation for the number of seeds germinating in each batch.

Accepted Answer

A) 1.652 
B) 1.568 
C) 1.587 
D) 1.632 
A) 1.652 
B) 1.568 
C) 1.587 
D) 1.632

Question 17

A machine has 9 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

Accepted Answer

A) 0.086 
B) 0.066 
C) 0.980 
D) 0.914 
A) 0.086 
B) 0.066 
C) 0.980 
D) 0.914

Question 18

The Columbia Power Company experiences power failures with a mean of µ = 0.210 per day. Find the probability that there are exactly two power failures in a particular day.

Accepted Answer

A) 0.085 
B) 0.027 
C) 0.018 
D) 0.036 
A) 0.085 
B) 0.027 
C) 0.018 
D) 0.036

Question 19

Find the mean of the given probability distribution.
-The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 1 & 0.13 \
2 & 0.12 \
3 & 0.16 \
4 & 0.13 \
5 & 0.15 \
6 & 0.31
\end{array}$$

Accepted Answer

A) 0.17 
B) 3.50 
C) 3.85 
D) 3.98 
A) 0.17 
B) 3.50 
C) 3.85 
D) 3.98

Question 20

Use the normal distribution to approximate the desired probability.
-Find the probability of selecting 9 or more girls.

Accepted Answer

A) 0.061 
B) 0.001 
C) 0.122 
D) 0.212 
A) 0.061 
B) 0.001 
C) 0.122 
D) 0.212

Answer the question. -Choosing 5 people (without replacement)from a group of 59 people, of which 15 are women, keeping track of the number of men chosen.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - $\mathrm { n } = 665 ; \mathrm { p } = .7$

Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.9. Find the probability that in a randomly selected year, the number of lightning strikes is 2.

Solve the problem. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - $n = 20 ; p = 3 / 5$

Provide an appropriate response. -Describe the differences in the Poisson and the binomial distribution.

Provide an appropriate response. -Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Provide an appropriate response. -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.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 94, p = 0.20

Assume that x is a random variable in a probability distribution with mean µ and standard deviation ?. Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 3, then increased by 5.

Solve the problem. -According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Solve the problem. -The probability of winning a certain lottery is 1/56,728. For people who play 517 times, find the standard deviation for the number of wins.

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 13. Find the standard deviation for the number of seeds germinating in each batch.

A machine has 9 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

The Columbia Power Company experiences power failures with a mean of µ = 0.210 per day. Find the probability that there are exactly two power failures in a particular day.

Find the mean of the given probability distribution. -The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. () 1 0.13 2 0.12 3 0.16 4 0.13 5 0.15 6 0.31

Use the normal distribution to approximate the desired probability. -Find the probability of selecting 9 or more girls.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 5: Probability Distributions

Answer the question. -Choosing 5 people (without replacement)from a group of 59 people, of which 15 are women, keeping track of the number of men chosen.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - n=665;p=.7\mathrm { n } = 665 ; \mathrm { p } = .7n=665;p=.7

Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.9. Find the probability that in a randomly selected year, the number of lightning strikes is 2.

Solve the problem. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - n=20;p=3/5n = 20 ; p = 3 / 5n=20;p=3/5

Provide an appropriate response. -Describe the differences in the Poisson and the binomial distribution.

Provide an appropriate response. -Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Provide an appropriate response. -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.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 94, p = 0.20

Assume that x is a random variable in a probability distribution with mean µ and standard deviation ?. Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 3, then increased by 5.

Solve the problem. -According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Solve the problem. -The probability of winning a certain lottery is 1/56,728. For people who play 517 times, find the standard deviation for the number of wins.

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 13. Find the standard deviation for the number of seeds germinating in each batch.

A machine has 9 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

The Columbia Power Company experiences power failures with a mean of µ = 0.210 per day. Find the probability that there are exactly two power failures in a particular day.

Find the mean of the given probability distribution. -The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. () 1 0.13 2 0.12 3 0.16 4 0.13 5 0.15 6 0.31

Use the normal distribution to approximate the desired probability. -Find the probability of selecting 9 or more girls.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - $\mathrm { n } = 665 ; \mathrm { p } = .7$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - $n = 20 ; p = 3 / 5$