# Stats Multiple Choice

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### c

Suppose that sixteen-ounce bags of chocolate chip cookies are produced with an actual mean weight of 16.1 ounces and a standard deviation of 0.1 ounce. The percentage of bags that will contain between 16.0 and 16.1 ounces is

a. 10
b. 16
c. 34
d. 68
e. none of the above

### e

Which statement is true for any density curve?

a. The bars must be of equal width.
b. It is symmetric.
c. It must either steadily rise or steadily fall, since it cannot do both.
d. One can use Table A (table of standard normal values) to find relative frequencies.
e. None of the above is correct.

### c

Increasing the frequencies in the tails of a distribution will:

a. Not affect the standard deviation as long as the increases are balanced on each side of the mean
b. not affect the standard deviation
c. Increase the standard deviation
d. reduce the standard deviation
e. none of the above

### a

Which of the following are true statements?
I. The area under a normal curve is always 1, regardless of the mean and standard deviation.
II. The mean is always equal to the median for any normal distribution.
III. The interquartile range for any normal curve extends from (mean-1 standard deviation) to (mean+1standard deviation)

a. I and II
b. I and III
c. II and III
d. I, II, and III
e. None of the above gives the correct set of true responses

### e

Pop1 and Pop2 are normal density curves with means and standard deviations mean1, st dev1, and mean2, st dev2, respectively. Suppose that mean1=mean2 and st dev1=2(st dev2). Consider these statements:

I. Pop1 has twice as many observations within one standard deviation of the mean as Pop2.
II. The density curve for Pop1 is taller than that of Pop2.
III. The density curves are centered around different numbers.
Which of these statements are correct?

a. I only
b. II only
c. III only
d. I and II only
e. None of the above gives the correct set of true responses

### b

A researcher wishes to calculate the average height of patients suffering from a particular disease. From patient record, the mean was computed as 156cm, and the standard deviation as 5cm. Further investigation reveals that the scale was misaligned, and that all readings are 2cm too large, for example, a patient whose height is really 180cm was measured as 182cm. Furthermore, the researcher would like to work with statistics based on meters. The correct mean and standard deviation are:

a. 1.56m, .05m
b. 1.54m, .05m
c. 1.56m, .03m
d. 1.58m, .05m
e. 1.58m, .07m

### c

A medical researcher collects health data on many women in each of several countries. One of the variables measure for each woman in the sudy is her weight in pounds. The following list gives the five-number summary for the weights of women in one of the countries.

Country A: 100, 110, 120, 160, 200

About what percentage of country A women weight between 110 and 200 pounds?

a. 50%
b. 65%
c. 75%
d. 85%
e. 95%

### e

The mediam age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. THe mediam age of the remaining four people in the room is:

a. 40 years
b. 30 years
c. 25 year
d. less than 30 years
e. Cannot be determined from the information given

### d

Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements of nine earthquakes gave the following readings:

4.5
L
5.5
H
8.7
8.9
6.0
H
5.2

Where L indicates that the earthquake had an intensity below 4.0 and an H indicates that the earthquake had an intensity above 9.0. The median earthwuake intensity of the sample is

a. Cannot be computed since all of the values are not known
b. 8.70
c. 5.75
d. 6.00
e. 6.47

### d

The probability of any outcome of a random phenomenon is

a. the precise degree of randomness present in the phenomenon
b. any number as long as it is between 0 and 1
c. Either 0 or 1, depending on whether or not the phenomenon can actually occur or not
d. The proportion of a very long series of repetitions on which the outcome occurs
e. none of the above

### a

A randomly elected student is asked to respond to yes, no, or maybe to the question, "Do you intend to vote in the next presidential election?" The sample space is {yes, no, maybe}. Which of the following represent a legitimate assignment of probabilities for this sample space?

a. 0.4, 0.4, 0.2
b. 0.6, 0.6, 0.4
c. 0.3, 0.3, 0.3
d. 0.5, 0.3, -0.2
e. None of the above

### c

If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that the card chosen is not a heart?

a. 0.25
b. 0.5
c. 0.75
d. 1
e. none of the above

### b

You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of .6 of winning. The probability that you win the next two matches is

a. 0.16
b. 0. 36
c. 0.4
d. 0.6
e. 1.2

### c

If P(A)=0.24 and P(B)=0.52 and A and B are independent, what is P(A or B)?

a. 0.1248
b. 0.28
c. 0.6352
d. 0.76
e. The answer cannot be determined from the information given.

### When two events share no outcomes.

What is meant by disjoint (mutually exclusive) events?

### When two events go along with each other to add up to 1.

Define complementary events

### c

Suppose we fit the least squares regression line to a set of data. What do we call any individual points with unusually large values of the residuals?

a. response variables
b. the slope
c. outliers
d. correlations
e. none of the above

### d

If removing an observation from a data set would have a marked change on the position of the LSRL fit to the data, what is the point called:

a. robust
b. a residual
c. a response
d. influential
e. none of the above

### c

Which of the following statements are correct?

I. Two variables that are strongly associated will have a correlation near 1
II. Regression requires an explanatory-response relationship, while correlation does not.
III. Even though the correlation between two variables may be high, in order to use the LSRL to predict, there needs to be an explanatory-response relationship between x and y.

a. I and II only
b. I and III only
c. II and III only
d. I, II, III
e. None of the above gives the complete set of true responses.

### c

Recent data show that states that spend an above-average amount of money X per pupil in high school tend to have below-average mean Verbal SAT scores Y of all students taking the SAT in the state. In other words, there is a negative association between X (spending per pupil) and Y (mean Verbal SAT score). High spending per pupil and low mean verbal SAT scores are particularly common in states that have a large percentage of all high school students takking the exam. Such states also tend to have a larger populations. The most plausible explanation for the observed association between X and Y is that

a. X causes Y. Overspending generally leads to extra, unnecessary programs, diverting attention from basic subjects. Inadequate training in these basic subjects generally leads to lower SAT scores.
b. Y causes X. Low SAT scores create concerns about the quality of education. This inevitably leads to additional spending to help solve the problem.
c. changes in X and Y are due to a common response to other variables. If a higher percentage of students take the exam, the average score will be lower. Also, states with larger populations have large urban areas where the cost of living is higher and more money is needed for expenses.
d. the association between X and Y is purely coincidental. it is implausible to believe the observed association could be anything other that accidental.

### b

A researcher notices that in a sample of adults, those that take larger amount of vitamin C have fewer illnesses. However, those that take larger amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables "amount of vitamin C taken" and "amount of exercise" are

a. skewed
b. confounded
c. common responses
d. symmetric

### d

What do we call a sample that consists of the entire population?

a. stratum
b. a multistage sample
c. a mistake. A sample can never be the entire population
d. a census
e. none of the above

### a

A member of Congress wants to know what his constituent think of proposed legislation on health insurance. His staff reports that 228 letters have been received on the subject, of which 193 oppose the legislation. What is the population in this situation?

a. the constituents
c. the 193 opposing the legislation
d. Congress
e. None of the above

### c

Which of the following is a method for improving the accuracy of a sample?

a. Use no more than 3 or 4 words in any question
b. When possible, avoid the use of human interviewers, relying on computerized dialing instead
c. Use large sample sizes
d. Use smaller sample sizes
e. None of the above.

### c

We say that the design of a study is biased if which of the following is true?

a. A racial or sexual preference
b. Random placebos have been used
c. certain outcomes are systematically favored.
d. The correlation is greater that 1 or less than -1
e. none of the above.

### a

Control groups are used in experiments in order to...

a. control the effects of lurking variables such as the placebo
b. control the subjects of a study so as to insure all participate equally
c. guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the experiment is conducted
d. achieve a proper and uniform level of randomization
e. none of theabove

### No, a treatment is not imposed

Suppose the Richmond-Times dispatch asks a sample of 150 Richmonders their opinions on the quality of life in Richmond.

is this study an experiment? Why or why not?

### d

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y=10+0.9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

a. 95
b. 85.5
c. 90
d. 95.5
e. none of the above

### b

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y=10+0.9x where y is the final exam score and x is the score on the first test. On the final exam Carla scored 98. What is the value of her residual?

a. 98
b. 2.5
c. -2.5
d. 0
e. none of the above

### b

All but one of the following statements contains a blinder. Which statement is correct?

a. The is a correlation of 0.54 between the position of a football player plays and his weight.
b. The correlation between planting rate and yield of corn was found to be r=0.23.
c. The correlation between the gas milage of a car and its weight is r=0.71 MPG
d. We found a high correlation (r=1.09) between the height and age of children.
e. We found a correlation of r=-.63 between gender and political party preference.

### no

In general, is correlation a resistant measure of association?

### no, influential points effect it.

Is the least-squares regression line resistant? Why?

### a

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

a. 0.3020
b. 0.2634
c. 0.2013
d. 0.5
e. 1
f. none of the above

### b

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the standard deviation of of the number of students in the sample who have experienced math anxiety is

a. 0.0160
b. 1.265
c. 0.2530
d. 1
e. .2070

### d

In a certain population, 40% of households have a total annual income of \$70,000. A simple random sample of 4 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of over \$70,000?

a. 0.34565
b. 0.4000
c. 0.5000
d. 0.5248
e. The answer cannot be computed from the information given

### a

A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications?

a. 16.20
b. 1.62
c. 4.02
d. 16.00
e. The answer cannot e computed from the information given.

### c

Which of the following are true statements?

I. The expected value of a geometric random variable is determined by the formula p(1-p)^n-1
II. If X is a geometric random variable and the probability of success is .85, then the probability distribution of X will be skewed left, snince 85 is closer to 1 than to 0.
III.. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

a. I only
b. II only
c. III only
d. I, II, and III
e. None of the above gives the complete set of true responses

### 1. set n trials 2. success or failure (2 outcomes) 3. independent trials 4. p always stays the same

Describe the four conditions that describe a binomial setting.

### c

Suppose X is a random variable with a mean. Suppose we observe X many times and keep track of the average of the observed values. The law of large numbers says that

a. The value of mean will get larger and larger as we observe X
b. As we observe X more and more, this average and the value of mean with get larger and larger.
c. This average will get closer and closer to the mean as we observe X more and more often.
d. as we observe X more and more, this average will get to be a larger and larger multiple of mean.
e. none of the above

### c

In a population of students, the number of calculators owned is a random variable X with P(X=0)=0.2, P(X=1)=0.6, and P(X=2)=0.2. The mean of this probability distribution is

a. 0
b. 2
c. 1
d. 0.5
e. The answer cannot be computed from the imformation given

### d

In a population of students, the number of calculators owned is a random variable X with P(X=0)=0.2, P(X=1)=0.6, and P(X=2)=0.2. The variance of this probability distribution is

a. 1
b. 0.63
c. 0.5
d. 0.4
e. the answer cannot be computed from the information given

### c

The number of calories in a one0ounce serving of a certain breakfast cereal is a random variable with mean 110. The number of calories in a full cup of whole milk is a random variable with mean 140. for breakfast you eat one ounce of the cereal with 1/2 cup of whole milk. Let Z be the random variable that represents the total number of calories in the breakfast. The mean of Z is

a. 110
b. 140
c. 180
d. 250
e. 195

### b

The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. What is the probability that the next report will weight less than 45g?

a. 0.1042
b. 0.1056
c. 9,3944
d. 0.0418
e. The answer cannot be computed from the information given

Example:
The content structure consists of multiple-choice questions related to statistics, each followed by a set of answer options and the correct answer.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Stats Multiple Choice

### 43 terms by Mrobinson

#### Study  only

Flashcards Flashcards

Scatter Scatter

Scatter Scatter

## Create a new folder

### c

Suppose that sixteen-ounce bags of chocolate chip cookies are produced with an actual mean weight of 16.1 ounces and a standard deviation of 0.1 ounce. The percentage of bags that will contain between 16.0 and 16.1 ounces is

a. 10
b. 16
c. 34
d. 68
e. none of the above

### e

Which statement is true for any density curve?

a. The bars must be of equal width.
b. It is symmetric.
c. It must either steadily rise or steadily fall, since it cannot do both.
d. One can use Table A (table of standard normal values) to find relative frequencies.
e. None of the above is correct.

### c

Increasing the frequencies in the tails of a distribution will:

a. Not affect the standard deviation as long as the increases are balanced on each side of the mean
b. not affect the standard deviation
c. Increase the standard deviation
d. reduce the standard deviation
e. none of the above

### a

Which of the following are true statements?
I. The area under a normal curve is always 1, regardless of the mean and standard deviation.
II. The mean is always equal to the median for any normal distribution.
III. The interquartile range for any normal curve extends from (mean-1 standard deviation) to (mean+1standard deviation)

a. I and II
b. I and III
c. II and III
d. I, II, and III
e. None of the above gives the correct set of true responses

### e

Pop1 and Pop2 are normal density curves with means and standard deviations mean1, st dev1, and mean2, st dev2, respectively. Suppose that mean1=mean2 and st dev1=2(st dev2). Consider these statements:

I. Pop1 has twice as many observations within one standard deviation of the mean as Pop2.
II. The density curve for Pop1 is taller than that of Pop2.
III. The density curves are centered around different numbers.
Which of these statements are correct?

a. I only
b. II only
c. III only
d. I and II only
e. None of the above gives the correct set of true responses

### b

A researcher wishes to calculate the average height of patients suffering from a particular disease. From patient record, the mean was computed as 156cm, and the standard deviation as 5cm. Further investigation reveals that the scale was misaligned, and that all readings are 2cm too large, for example, a patient whose height is really 180cm was measured as 182cm. Furthermore, the researcher would like to work with statistics based on meters. The correct mean and standard deviation are:

a. 1.56m, .05m
b. 1.54m, .05m
c. 1.56m, .03m
d. 1.58m, .05m
e. 1.58m, .07m

### c

A medical researcher collects health data on many women in each of several countries. One of the variables measure for each woman in the sudy is her weight in pounds. The following list gives the five-number summary for the weights of women in one of the countries.

Country A: 100, 110, 120, 160, 200

About what percentage of country A women weight between 110 and 200 pounds?

a. 50%
b. 65%
c. 75%
d. 85%
e. 95%

### e

The mediam age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. THe mediam age of the remaining four people in the room is:

a. 40 years
b. 30 years
c. 25 year
d. less than 30 years
e. Cannot be determined from the information given

### d

Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements of nine earthquakes gave the following readings:

4.5
L
5.5
H
8.7
8.9
6.0
H
5.2

Where L indicates that the earthquake had an intensity below 4.0 and an H indicates that the earthquake had an intensity above 9.0. The median earthwuake intensity of the sample is

a. Cannot be computed since all of the values are not known
b. 8.70
c. 5.75
d. 6.00
e. 6.47

### d

The probability of any outcome of a random phenomenon is

a. the precise degree of randomness present in the phenomenon
b. any number as long as it is between 0 and 1
c. Either 0 or 1, depending on whether or not the phenomenon can actually occur or not
d. The proportion of a very long series of repetitions on which the outcome occurs
e. none of the above

### a

A randomly elected student is asked to respond to yes, no, or maybe to the question, "Do you intend to vote in the next presidential election?" The sample space is {yes, no, maybe}. Which of the following represent a legitimate assignment of probabilities for this sample space?

a. 0.4, 0.4, 0.2
b. 0.6, 0.6, 0.4
c. 0.3, 0.3, 0.3
d. 0.5, 0.3, -0.2
e. None of the above

### c

If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that the card chosen is not a heart?

a. 0.25
b. 0.5
c. 0.75
d. 1
e. none of the above

### b

You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of .6 of winning. The probability that you win the next two matches is

a. 0.16
b. 0. 36
c. 0.4
d. 0.6
e. 1.2

### c

If P(A)=0.24 and P(B)=0.52 and A and B are independent, what is P(A or B)?

a. 0.1248
b. 0.28
c. 0.6352
d. 0.76
e. The answer cannot be determined from the information given.

### When two events share no outcomes.

What is meant by disjoint (mutually exclusive) events?

### When two events go along with each other to add up to 1.

Define complementary events

### c

Suppose we fit the least squares regression line to a set of data. What do we call any individual points with unusually large values of the residuals?

a. response variables
b. the slope
c. outliers
d. correlations
e. none of the above

### d

If removing an observation from a data set would have a marked change on the position of the LSRL fit to the data, what is the point called:

a. robust
b. a residual
c. a response
d. influential
e. none of the above

### c

Which of the following statements are correct?

I. Two variables that are strongly associated will have a correlation near 1
II. Regression requires an explanatory-response relationship, while correlation does not.
III. Even though the correlation between two variables may be high, in order to use the LSRL to predict, there needs to be an explanatory-response relationship between x and y.

a. I and II only
b. I and III only
c. II and III only
d. I, II, III
e. None of the above gives the complete set of true responses.

### c

Recent data show that states that spend an above-average amount of money X per pupil in high school tend to have below-average mean Verbal SAT scores Y of all students taking the SAT in the state. In other words, there is a negative association between X (spending per pupil) and Y (mean Verbal SAT score). High spending per pupil and low mean verbal SAT scores are particularly common in states that have a large percentage of all high school students takking the exam. Such states also tend to have a larger populations. The most plausible explanation for the observed association between X and Y is that

a. X causes Y. Overspending generally leads to extra, unnecessary programs, diverting attention from basic subjects. Inadequate training in these basic subjects generally leads to lower SAT scores.
b. Y causes X. Low SAT scores create concerns about the quality of education. This inevitably leads to additional spending to help solve the problem.
c. changes in X and Y are due to a common response to other variables. If a higher percentage of students take the exam, the average score will be lower. Also, states with larger populations have large urban areas where the cost of living is higher and more money is needed for expenses.
d. the association between X and Y is purely coincidental. it is implausible to believe the observed association could be anything other that accidental.

### b

A researcher notices that in a sample of adults, those that take larger amount of vitamin C have fewer illnesses. However, those that take larger amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables "amount of vitamin C taken" and "amount of exercise" are

a. skewed
b. confounded
c. common responses
d. symmetric

### d

What do we call a sample that consists of the entire population?

a. stratum
b. a multistage sample
c. a mistake. A sample can never be the entire population
d. a census
e. none of the above

### a

A member of Congress wants to know what his constituent think of proposed legislation on health insurance. His staff reports that 228 letters have been received on the subject, of which 193 oppose the legislation. What is the population in this situation?

a. the constituents
c. the 193 opposing the legislation
d. Congress
e. None of the above

### c

Which of the following is a method for improving the accuracy of a sample?

a. Use no more than 3 or 4 words in any question
b. When possible, avoid the use of human interviewers, relying on computerized dialing instead
c. Use large sample sizes
d. Use smaller sample sizes
e. None of the above.

### c

We say that the design of a study is biased if which of the following is true?

a. A racial or sexual preference
b. Random placebos have been used
c. certain outcomes are systematically favored.
d. The correlation is greater that 1 or less than -1
e. none of the above.

### a

Control groups are used in experiments in order to...

a. control the effects of lurking variables such as the placebo
b. control the subjects of a study so as to insure all participate equally
c. guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the experiment is conducted
d. achieve a proper and uniform level of randomization
e. none of theabove

### No, a treatment is not imposed

Suppose the Richmond-Times dispatch asks a sample of 150 Richmonders their opinions on the quality of life in Richmond.

is this study an experiment? Why or why not?

### d

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y=10+0.9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

a. 95
b. 85.5
c. 90
d. 95.5
e. none of the above

### b

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y=10+0.9x where y is the final exam score and x is the score on the first test. On the final exam Carla scored 98. What is the value of her residual?

a. 98
b. 2.5
c. -2.5
d. 0
e. none of the above

### b

All but one of the following statements contains a blinder. Which statement is correct?

a. The is a correlation of 0.54 between the position of a football player plays and his weight.
b. The correlation between planting rate and yield of corn was found to be r=0.23.
c. The correlation between the gas milage of a car and its weight is r=0.71 MPG
d. We found a high correlation (r=1.09) between the height and age of children.
e. We found a correlation of r=-.63 between gender and political party preference.

### no

In general, is correlation a resistant measure of association?

### no, influential points effect it.

Is the least-squares regression line resistant? Why?

### a

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

a. 0.3020
b. 0.2634
c. 0.2013
d. 0.5
e. 1
f. none of the above

### b

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the standard deviation of of the number of students in the sample who have experienced math anxiety is

a. 0.0160
b. 1.265
c. 0.2530
d. 1
e. .2070

### d

In a certain population, 40% of households have a total annual income of \$70,000. A simple random sample of 4 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of over \$70,000?

a. 0.34565
b. 0.4000
c. 0.5000
d. 0.5248
e. The answer cannot be computed from the information given

### a

A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications?

a. 16.20
b. 1.62
c. 4.02
d. 16.00
e. The answer cannot e computed from the information given.

### c

Which of the following are true statements?

I. The expected value of a geometric random variable is determined by the formula p(1-p)^n-1
II. If X is a geometric random variable and the probability of success is .85, then the probability distribution of X will be skewed left, snince 85 is closer to 1 than to 0.
III.. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

a. I only
b. II only
c. III only
d. I, II, and III
e. None of the above gives the complete set of true responses

### 1. set n trials 2. success or failure (2 outcomes) 3. independent trials 4. p always stays the same

Describe the four conditions that describe a binomial setting.

### c

Suppose X is a random variable with a mean. Suppose we observe X many times and keep track of the average of the observed values. The law of large numbers says that

a. The value of mean will get larger and larger as we observe X
b. As we observe X more and more, this average and the value of mean with get larger and larger.
c. This average will get closer and closer to the mean as we observe X more and more often.
d. as we observe X more and more, this average will get to be a larger and larger multiple of mean.
e. none of the above

### c

In a population of students, the number of calculators owned is a random variable X with P(X=0)=0.2, P(X=1)=0.6, and P(X=2)=0.2. The mean of this probability distribution is

a. 0
b. 2
c. 1
d. 0.5
e. The answer cannot be computed from the imformation given

### d

In a population of students, the number of calculators owned is a random variable X with P(X=0)=0.2, P(X=1)=0.6, and P(X=2)=0.2. The variance of this probability distribution is

a. 1
b. 0.63
c. 0.5
d. 0.4
e. the answer cannot be computed from the information given

### c

The number of calories in a one0ounce serving of a certain breakfast cereal is a random variable with mean 110. The number of calories in a full cup of whole milk is a random variable with mean 140. for breakfast you eat one ounce of the cereal with 1/2 cup of whole milk. Let Z be the random variable that represents the total number of calories in the breakfast. The mean of Z is

a. 110
b. 140
c. 180
d. 250
e. 195

### b

The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. What is the probability that the next report will weight less than 45g?

a. 0.1042
b. 0.1056
c. 9,3944
d. 0.0418
e. The answer cannot be computed from the information given

Example:
user
The content structure consists of multiple-choice questions related to statistics, each followed by a set of answer options and the correct answer.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS