One of the assumptions used when analyzing a simple truss is that the members are joined together by __________.

Answer: Smooth pins

What will be the easiest way to determine the force reaction BZ ?

Answer: Vector equation MA = 0

A plate is supported by a ball-and-socket joint at A, a roller joint at B, and a cable at C. How many unknown support reactions are there in this problem?

Answer: five forces

When doing a 3-D problem analysis, you have ________ scalar equations of equilibrium.

Answer: 6

If a support prevents translation of a body, then the support exerts a ___________ on the body.

Answer: Force

If a support prevents rotation of a body about an axis, then the support exerts a ________ on the body about that axis.

Answer: Couple moment

The three scalar equations, FX = FY = MO = 0, are ____ equations of equilibrium in two dimensions.

Answer: The most commonly used

The original force and couple system and an equivalent force-couple system have the same _____ effect on a body.

Answer: external

Internal forces are _________ shown on the free body diagram of a whole body.

Answer: Never

If a support prevents translation of a body, then the support exerts a ___________ on the body.

Answer: Force

A general system of forces and couple moments acting on a rigid body can be reduced to a ___ .

Answer: single force and a single moment

The moment of a couple is called a _________ vector.

Answer: free

In statics, a couple is defined as __________ separated by a perpendicular distance.

Answer: two forces of equal magnitude acting in opposite directions

If r = {1 i + 2 j} m and F = {10 i + 20 j + 30 k} N, then the moment of F about the y-axis is ____ N·m.

Answer: -30

The triple scalar product u • ( r F ) results in

Answer: a scalar quantity ( + or - ).

When determining the moment of a force about a specified axis, the axis must be along _____________.

Answer: any line in 3-D space

If a particle has 3-D forces acting on it and is in static equilibrium, the components of the resultant force ( Fx, Fy, and Fz ) ___ .

Answer: have to equal zero, e.g., 0 i + 0 j + 0 k

If a force of magnitude F can be applied in four different 2-D configurations (P,Q,R, & S), select the cases resulting in the maximum and minimum torque values on the nut. (Max, Min).

Answer: (Q, S) (perpendicular to nut/wrench)

For a frictionless pulley and cable, tensions in the cable (T1 and T2) are related as _____ .

Answer: T1 = T2

When a particle is in equilibrium, the sum of forces acting on it equals ___ . 

Answer: Zero

If a dot product of two non-zero vectors equals -1, then the vectors must be ________ to each other.

Answer: Collinear but pointing in the opposite direction

If a dot product of two non-zero vectors is 0, then the two vectors must be _____________ to each other.

Answer: Perpendicular

The dot product of two vectors results in a _________ quantity.

Answer: scalar

The dot product of two vectors P and Q is defined as

Answer: P Q cos (theta)

The height of a building, measured in feet, is an example of

a. categorical data

b. either categorical or quantitative data

c. feet data

d. quantitative data

Answer: d. quantitative data

The weight of a candy bar in ounces is an example of

a. categorical data

b. either categorical or quantitative data

c. weight data

d. quantitative data

Answer: d. quantitative data

Which of the following variables use the ratio scale of measurement?

a. social security number

b. temperature

c. gender

d. income

Answer: d. income

Which scale of measurement can be either numeric or nonnumeric?

a. nominal

b. ratio

c. interval

d. None of these alternatives is correct.

Answer: a. nominal

Which of the following is a scale of measurement?

a. ratio

b. primal

c. divisional

d. remedial

Answer: a. ratio

Which of the following is not a scale of measurement?

a. nominal

b. ordinal

c. interval

d. primal

Answer: d. primal

In a data set, the number of elements will always be the same as the number of

a. independent variables

b. observations

c. data points

d. dependent variables

Answer: b. observations

The scale of measurement that is simply a label for the purpose of identifying the attribute of an element is the

a. ratio scale

b. nominal scale

c. ordinal scale

d. interval scale

Answer: b. nominal scale

Since a sample is a subset of the population, the sample mean

a. is always smaller than the mean of the population

b. is always larger than the mean of the population

c. must be equal to the mean of the population

d. can be larger, smaller, or equal to the mean of the population

Answer: d. can be larger, smaller, or equal to the mean of the population

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. must be more than 22, since the population is always larger than the sample

b. must be less than 22, since the sample is only a part of the population

c. could not be 22

d. could be larger, smaller, or equal to 22

Answer: d. could be larger, smaller, or equal to 22

In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent

a. categorical data

b. quantitative data

c. either categorical or quantitative data

d. since the numbers are sequential, the data is quantitative

Answer: a. categorical data

The process of analyzing sample data in order to draw conclusions about the characteristics of a population is called

a. Data and Statistics

b. statistical inference

c. data analysis

d. data summarization

Answer: b. statistical inference

The Department of Transportation of a city has noted that on the average there are 17 accidents per day. The average number of accidents is an example of

a. Data and Statistics

b. statistical inference

c. a sample

d. a population

Answer: a. Data and Statistics

The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of

a. a sample

b. Data and Statistics

c. statistical inference

d. an experiment

Answer: b. Data and Statistics

A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 24 years. This is an example of

a. a census

b. Data and Statistics

c. an experiment

d. statistical inference

Answer: d. statistical inference

Five hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The five hundred residents in this study is an example of a(n)

a. census

b. sample

c. observation

d. population

Answer: b. sample

In a sample of 400 students in a university, 80, or 20%, are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of

a. a sample

b. a population

c. statistical inference

d. Data and Statistics

Answer: c. statistical inference

One hundred students from a large university were asked about their opinion on the new health care program. The 100 represents

a. a sample

b. a population

c. statistical inference

d. data and statistics

Answer: a. a sample

A portion of the population selected to represent the population is called

a. statistical inference

b. Data and Statistics

c. a census

d. a sample

Answer: d. a sample

The collection of all elements of interest in a particular study is

a. the population

b. the sampling

c. statistical inference

d. Data and Statistics

Answer: a. the population

Statistical inference

a. refers to the process of drawing inferences about the sample based on the characteristics of the population

b. is the same as Data and Statistics

c. is the process of drawing inferences about the population based on the information taken from the sample

d. is the same as a census

Answer: c. is the process of drawing inferences about the population based on the information taken from the sample

The summaries of data, which may be tabular, graphical, or numerical, are referred to as

a. inferential statistics

b. Data and Statistics

c. statistical inference

d. report generation

Answer: b. Data and Statistics

Statistical studies in which researchers control variables of interest are

a. experimental studies

b. control observational studies

c. non-experimental studies

d. observational studies

Answer: a. experimental studies

Statistical studies in which researchers do not control variables of interest are

a. experimental studies

b. uncontrolled experimental studies

c. not of any value

d. observational studies

Answer: d. observational studies

Data collected over several time periods are

a. time series data

b. time controlled data

c. crossectional data

d. time crossectional data

Answer: a. time series data

Data collected at the same, or approximately the same, point in time are

a. time series data

b. approximate time series data

c. crossectional data

d. approximate data

Answer: c. crossectional data

Income is an example of

a. categorical data

b. either categorical or quantitative data

c. dollar data

d. quantitative data

Answer: d. quantitative data

Arithmetic operations are inappropriate for

a. categorical data

b. quantitative data

c. both categorical and quantitative data

d. large data sets

Answer: a. categorical data

For ease of data entry into a university database, 1 denotes that the student is an undergraduate and 2 indicates that the student is a graduate student. In this case data are

a. categorical

b. quantitative

c. either categorical or quantitative

d. neither categorical nor quantitative

Answer: a. categorical

Temperature is an example of

a. a categorical variable

b. a quantitative variable

c. either a quantitative or categorical variable

d. neither a quantitative nor categorical variable

Answer: b. a quantitative variable

Social security numbers consist of numeric values. Therefore, social security is an example of

a. a quantitative variable

b. either a quantitative or a categorical variable

c. an exchange variable

d. a categorical variable

Answer: d. a categorical variable

Ordinary arithmetic operations are meaningful

a. only with categorical data

b. only with quantitative data

c. either with quantitative or categorical data

d. None of these alternatives is correct.

Answer: b. only with quantitative data

The 2000 census form asked 53 detailed questions, such as: "Do you have complete plumbing facilities in this house, apartment, or mobile home; hot and cold piped water, a flush toilet, and bathtub or shower?" The form also asked the questions about income (in dollars, broken down by source) and about whether any "physical, mental, or emotional condition causes difficulty in learning, remembering, or concentrating." Some members of Congress objected to these questions, even though Congress had approved them.

Which of the following statements, do you think, can be a valid reason of the objection raised by some members of the Congress, against some of the questions in the form?

A.

Some of the questions in the form were not in the interest of the Congress.

B.

Some of the questions in the form were not valid.

C.

Some of the questions in the form seem to invade privacy of the people.

Answer: C.

Some of the questions in the form seem to invade privacy of the people.

Your college or university has an institutional review board that screens all studies that use human subjects. Which of the following should be the duties of the board?

A.

Protect the rights and welfare of human subjects recruited to participate in research activities.

B.

Decide whether a proposed study is statistically sound.

C.

Put more proposals in the minimal-risk category to speed the work in the event of work overload.

D.

Decide whether a proposed study will produce valuable information.

E.

Review the consent forms to ensure that subjects are informed about the nature of the study and potential risks.

Answer: E.

Review the consent forms to ensure that subjects are informed about the nature of the study and potential risks.

In which of the circumstances below would you allow collecting personal information without the subjects' consent?

A.

A social psychologist pretends to be converted to membership in a religious group and attends private meetings to study the behavior patterns of members.

B.

A social psychologist attends public meetings of a religious group to study the behavior patterns of members.

C.

A government agency takes a random sample of income tax returns to obtain information on the average income of people in different occupations. Only the incomes and occupations are recorded from the returns, not the names.

Answer: C.

A government agency takes a random sample of income tax returns to obtain information on the average income of people in different occupations. Only the incomes and occupations are recorded from the returns, not the names.

One of the most important nongovernment surveys in the United States is the General Social Survey. The GSS regularly monitors public opinion on a wide variety of political and social issues. Interviews are conducted in person in the subject's home. 
A subject's responses to GSS questions are:

A.

Confidential

B.

Both confidential and anonymous

C.

Anonymous

Answer: A.

Confidential

Some people think that the law should require that all political poll results be made public. Otherwise, the possessors of poll results can use the information to their own advantage. They can act on the information, release only selected parts of it, or time the release for best effect. A candidate's organization replies that they are paying for the poll in order to gain information for their own use, not to amuse the public. 
Which of the following statements do you think is appropriate in reference to the scenario?

A.

The polling organizations can modify the information to their benefit and then make it public.

B.

The polling organizations can provide incomplete information, if they do not want to reveal complete information.

C.

The polling organizations should provide true information if they wish to make it public.

Answer: C.

The polling organizations should provide true information if they wish to make it public.

Error committed by rejecting a true null hypothesis

Answer: Type I error

Error committed by failing to reject a false null hypothesis

Answer: Type II error

The standard deviation of the distribution of sample means

Answer: Standard error of the mean

The quotient of the frequency at which a given characteristic occurs in a sample and the number of items in the sample

Answer: Sample proportion

If a null hypothesis is not rejected at the .05 level of significance, the p-value is bigger than 0.05

Answer: True

The rejection and nonrejection regions are divided by a point called the critical value

Answer: True

When using the p-value to test hypotheses, the null hypothesis would be rejected if

Answer: the p-value is less than the significance level

The probability of getting a test statistic as extreme as the observed test statistic computed from the sample data under the assumption that the null hypothesis is true is called the

Answer: p-value

If the calculated test statistic falls in the rejection region, the statistical action is to

Answer: reject the null hypothesis

A hypothesis demonstrated in an indirect way using the hypothesis test. If the null hypothesis is rejected, this hypothesis is accepted.

Answer: Alternative hypothesis

A hypothesis is a claim or assumption about an unknown population parameter

Answer: Hypothesis

Hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error

Answer: null hypothesis

Type II error is committed when

Answer: the null hypothesis is false and it is not rejected

Type I error is committed when

Answer: the null hypothesis is true and is rejected

Generally speaking, new hypotheses that business researchers want to "prove" are stated in the

Answer: alternate hypothesis

The probability of committing a Type I error is

Answer: the level of significance

A statistical hypotheses consists of two parts

Answer: a null hypothesis and an alternate hypothesis

Residents who own a house in a particular city were divided into 15 groups based on the location of their house. A random sample of ten residents from each of the 15 groups was selected to be interviewed. What type of sampling plan is being used?

a. Cluster sampling

b. Judgment sampling

c. Stratified random sampling

d. Systematic sampling

Answer: c. Stratified random sampling

For which of the following sampling methods can the sampling distribution of the sample statistics generally be identified?

a. cluster sampling

b. simple random sampling

c. systematic sampling

d. All of these choices are correct.

Answer: d. All of these choices are correct.

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into ten sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

a. Systematic sampling

b. Judgment sampling

c. Stratified random sampling

d. Cluster sampling

Answer: d. Cluster sampling

A sample chosen by stratified random sampling involves:

a. randomly selecting one of the first k elements in an ordered population, and then selecting every kth element in the population thereafter.

b. selecting a simple random sample of clusters from the available clusters in the population.

c. selecting a simple random sample from each of a given number of strata formed from the elements in the population.

d. a sample chosen by a knowledgeable person on the subject of the study.

Answer: c. selecting a simple random sample from each of a given number of strata formed from the elements in the population.

A random sample of 150 individuals who purchased a computer was taken. The survey determined that 70 of the individuals purchased Brand D. Which of the following is an unbiased estimate of the population proportion of all computers purchased that are Brand D?

a. .53

b. 70

c. The population proportion is not known so an unbiased estimate cannot be determined.

d. .47

Answer: d. .47

If a random sample of size n = 20 is taken from a normal distribution with a mean μ, which of the following would be an unbiased estimator for μ?

a.p̂

b. ?

c. x̄

d. s

Answer: c. x̄

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population.

a. .2939

b. .7061

c. .1368

d. .8632

Answer: a. .2939

Suppose s random sample of 20 observations is taken from an infinite population. The sampling distribution of p̂ is

a. not normal since n < 30

b. approximately uniform because p is always normally distributed

c. approximately normal if np > 30 and n(1 - p) > 30

d. approximately normal if np ≤ 5 and n(1 - p)≤ 5

Answer: d. approximately normal if np ≤ 5 and n(1 - p)≤ 5

The proportion of students at a university who pass a biology class is p =.86. If 50 students are randomly selected, what is the probability that at least 75% of them have passed the class?

a. .9638

b. .9875

c. .0362

d. .0125

Answer: b. .9875

A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12?

a. .60 and.14

b. 192 and 45

c. .60 and.02

d. 320 and.02

Answer: a. .60 and.14

If the sample size is increased, the standard error of the sampling distribution of x̄ will

a. It depends on the data being studied.

b. remain the same.

c. increase.

d. decrease.

Answer: d. decrease.

Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000?

a. 0.1465

b. 0.0371

c. 0.2005

d. 0.0827

Answer: c. 0.2005

A sample of 240 is selected from a finite population of 500. If the standard deviation of the population is 44, what is the standard error of the sample mean?

a. 4.20

b. 1.42

c. 2.05

d. 2.84

Answer: c. 2.05

When can the central limit theorem be used to approximate the sampling distribution of x̄ by a normal curve?

a. It can be used when the standard deviation of the population is normally distributed.

b. It can be used only when the population distribution is normal.

c. It can be used when the population distribution is not normal and n is greater than 30.

d. It can be used when the population is skewed and n is less than 20.

Answer: c. It can be used when the population distribution is not normal and n is greater than 30.

Which of the following is an unbiased point estimator?

a. n is an unbiased estimator of x̄

b. s is an unbiased estimator of sigma

c. All of these choices are correct.

d. x̄ is an unbiased estimator of μ

Answer: d. x̄ is an unbiased estimator of μ

The sample mean, x̄, obtained from repeated samples of the same size from a population is

a. a random variable.

b. always equal to 0.

c. exactly equal to the population mean.

d. always smaller than the population mean.

Answer: a. a random variable.

Given the sampling distribution of the sample mean shown here, which of the following values is a reasonable estimate for the population mean?

(highest bar is at 300)

a. 280

b. 300

c. 0.27

d. 320

Answer: b. 300

The sampling distribution describes the:

a. sample size.

b. long-run behavior of a statistic.

c. short-term behavior of the population.

d. population proportion.

Answer: b. long-run behavior of a statistic.

Suppose 8 out of 26 cars that pass a radar station are exceeding the speed limit. If the population proportion of cars that exceed the speed limit is .42, what is the value of p̂?

a. .69

b. .31

c. 8

d. .42

Answer: b. .31

A university is interested in the average age of its students. A simple random sample of 30 students was selected. The following descriptive statistics for their ages were compted: x̄ =20.8 and s^2=8.4. What is a point estimate of the population standard deviation for age?

a. 8.4

b. 20.8

c. 70.6

d. 2.9

Answer: d. 2.9

A simple random sample of 8 high school student's ACT scores gave the following data.

27, 30, 20, 29, 28, 36, 34, 31

What is a point estimate for μ, the mean test score for the population?

a. 235

b. 4.84

c. 29.38

d. A point estimate cannot be computed since the data for the whole population are not available.

Answer: c. 29.38

A dealership is interested in the population proportion of new vehicle purchases that are gold in color. Which of the following represents the sample statistic of interest?

a.(p̂)

b. μ

c. n

d. s

Answer: a.(p̂)

Starting salaries of a sample of five management majors along with their genders are shown below.

Employee|Salary($1000s)|M/F

1 | 30 | F

2 | 28 | M

3 | 22 | F

4 | 26 | F

5 | 19 | M

If we select simple random samples of size 2 from the given data, what is the probability of any of the five employees being selected first?

a. 0.40

b. 0.20

c. 0.50

d. 0.10

Answer: b. 0.20

A simple random sample of size 5 from an infinite population is to be selected. Each possible sample should have:

a. a probability of .2 of being selected.

b. a different probability of being selected.

c. a probability of .5 of being selected.

d. the same probability of being selected.

Answer: d. the same probability of being selected.

When the selection of one element from the population influences the selection of another element, the sample:

a. was selected using computer-generated random numbers.

b. contains selection bias.

c. is from a finite population.

d. is a simple random sample.

Answer: b. contains selection bias.

The number of simple random samples of size 20 that can be selected from a finite population of size 25 is:

a. 53,130

b. 1

c. 20

d. 120

Answer: a. 53,130

The symbol p typically represents a:

a. mean.

b. proportion.

c. standard deviation.

d. sample size.

Answer: b. proportion.

The CEO of a large corporation is interested in the average salary of all managers for his large corporation. A sample of 500 managers found the average salary to be $56,500. Which of the following statements is correct?

a. The average salary for all the managers will also be $56,500.

b. The average salary for the 500 managers can be used to estimate the average salary for all managers.

c. The population size is 500 managers.

d. The value $56,500 is a parameter.

Answer: b. The average salary for the 500 managers can be used to estimate the average salary for all managers.

The population mean is represented by the symbol:

a.x̄

b. sigma

c. S

d. μ

Answer: d. μ

The time it takes to completely clean an office building follows an exponential distribution with a mean of 135 minutes. What is the probability of cleaning an office building in 135 minutes or less?

a. .6321

b. .50

c. .3679

d. 1.00

Answer: a. .6321

Which of the following distributions is not symmetric?

a. Normal

b. All of these choices distributions are symmetric

c. Exponential

d. Standard normal

Answer: c. Exponential

Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours?

a. .5105

b. .5756

c. .4244

d. .0651

Answer: d. .0651

What is the mean of x for the exponential distribution, f(x)=(1/2)e^-x/2, x ≥ 0?

a. 1.36

b. 0

c. .5

d. 2

Answer: d. 2

The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that 45 or fewer rooms are occupied on a given day?

a. .5948

b. .5000

c. .9909

d. .4052

Answer: b. .5000

When using the normal approximation to the binomial, what is the standard deviation for a binomial probability distribution with p =.3 and n = 145?

a. 43.5

b. 5.52

c. 11.5

d. 30.45

Answer: b. 5.52

The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that at least 80% of the suites are occupied on a given day?

a. .1662

b. .9908

c. .5714

d. Not enough information is give to answer the question.

Answer: b. .9908

Which of the following represents the mean of the normal distribution used to approximate a binomial distribution?

a. μ=√np(1-p)

b. 0

c. μ=np

d. μ=n(1-p)

Answer: c. μ=np

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.9370?

a. 1.96

b. - 1.53

c. 1.50

d. .8264

Answer: b. - 1.53

If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, which of the following probabilities is not correct?

a. P(x ≤ 1) =.8413

b. P(x < 2) =.9772

c. P(x ≥ 1) =.1587

d. P(x = 0) =.50

Answer: d. P(x = 0) =.50

A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000?

a. .9999

b. .5000

c. .0885

d. .9115

Answer: c. .0885

Suppose a preliminary screening is given to prospective student athletes at a university to determine whether they would qualify for a scholarship. The scores are approximately normal with a mean of 85 and a standard deviation of 20. If the range of possible scores is 0 to 100, what percentage of students has a score less than 85?

a. 50%

b. 100%

c. 8.5%

d. 98.34%

Answer: a. 50%

The normal distribution is symmetric about:

a. the standard deviation.

b. 0

c. the mean.

d. 1

Answer: c. the mean.

A production line fills 64 ounce bottles of juice uniformly according to the following probability density function.

F(x)={4 for 63.85≤64.10}

{0 elsewhere}

What is the probability that the bottle will be filled between 63.90 and 64 ounces?

a. .25

b. .50

c. .16

d. .4

Answer: d. .4

Consider the continuous random variable x, which has a uniform distribution over the interval from 110 to 150. The probability that x will take on a value between 120 and 125 is:

a. .025

b. .50

c. .125

d. .20

Answer: c. .125

Let x be a uniform random variable on the interval 1≤x≤6. What is the standard deviation of x?

a. 1.44

b. 2.08

c. .2

d. 3.5

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is:

a. 75

b. .03

c. 30

d. 235

Answer: d. 235

What is the P(10≤x≤30) for a uniform random variable defined on the interval 0 to 40?

a. .025

b. .5

c. .05

d. 0

Answer: b. .5

A local retailer received a shipment of 20 items that included 6 defective and 14 nondefective items. In the inspection of the shipment, a sample of 8 items will be selected and tested. The mean number of defective items is:

a. 2.4

b. 5.6

c. .3

d. 6

Answer: a. 2.4

Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0?

a. .0001

b. .9333

c. .6667

d. .0667

Answer: d. .0667

A retailer received seven new items from the manufacturer. Four of the items were damaged in transit. The retailer sold three items to five customers. Which of the following probability distributions would be useful in this situation?

a. Poisson probability distribution

b. Binomial probability distributions

c. Uniform probability distribution

d. Hypergeometric probability distribution

Answer: d. Hypergeometric probability distribution

An air traffic controller has noted that it clears an average of 7 planes per hour for landing. What is the probability that during the next two hours exactly 15 planes will be cleared for landing?

a. .0651

b. .0033

c. .0989

d. Not enough information is given to answer the problem.

Answer: c. .0989

A manufacturer is interested in the number of flaws occurring in each 30 yards of material. The random variable representing the number of major flaws satisfies which of the following probability distributions?

a. Binomial

b. Not enough information is given to answer this question.

c. Normal

d. Poisson

Answer: d. Poisson

The random variable x is the number of vehicles that pass through an intersection in a 30 minute interval. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 30 minutes is 9. What is the expected value of the random variable x?

a. 3

b. 2.7

c. 9

d. 30

Answer: c. 9

Let x be a Poisson random variable with mean = 3. What is f(2)?

a. 1.732

b. .1804

c. .2240

d. .4232

Answer: c. .2240

Of the passengers on a 757 airliner, 40% are female. A random sample of 25 passengers is selected. What is the expected number of female passengers in the sample?

a. 40

b. 10

c. 6

d. 25

Answer: b. 10

A binomial experiment is conducted in which 30 dishwashers are randomly selected from a production plant and tested to determine whether or not they function properly. Any specific dishwasher will work properly with a probability of p =.98. What is the random variable in this experiment?

a. The number of dishwashers that work properly from the 30 selected

b. One dishwasher and whether it works properly

c. The 30 dishwashers

d. The probability that the dishwasher works properly

Answer: a. The number of dishwashers that work properly from the 30 selected

Twelve percent of the customers of a bank overdraw their accounts at least once a month. A sample of eight customers is selected. What is the probability that exactly two customers in the sample will overdraw their account this month?

a. .939

b. .187

c. .28

d. 0

Answer: b. .187

Suppose a binomial random variable consists of 9 trials with a success of probability of .4. What are the mean and standard deviation for this binomial random variable?

a. The mean is 2 and the standard deviation is 2.16.

b. The mean is 3.6 and the standard deviation is 1.47.

c. The mean and standard deviation cannot be calculated from the information given.

d. The mean is .4 and the standard deviation is 1.

Answer: b. The mean is 3.6 and the standard deviation is 1.47.

A production process produces 2% defective parts. A sample of nine parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

a. .0200

b. .9994

c. .0125

d. .9875

Answer: c. .0125

Suppose a random variable t has a probability distribution defined by f(t) = t/20 for t = 2, 4, 6, and 8. What is the expected value for t?

a. 1.5

b. 2

c. 6

d. 5

Answer: c. 6

The variance is a weighted average of the:

a. squared deviations from the median

b. square root of the deviations from the mean

c. squared deviations from the mean

d. square root of the deviations from the median

Answer: c. squared deviations from the mean

Assume the number of customers who order a dessert with their meal on a given night at a local restaurant has the probability distribution given below.

x | f(x)

3 .25

4 .55

5 .15

6 .05

The variance for the random variable x is:

a. .77

b. .60

c. .36

d. 4

Answer: b. .60

The number of vehicle thefts in the parking lot of a shopping mall varies from month to month. Assume that the number of thefts(x) at the shopping mall has the following probability distribution.

x | f(x)

0 .60

1 .25

2 .15

3 .05

The mean number of thefts per month is:

a. 6

b. .175

c. 1.5

d. .70

Answer: d. .70

A production manager has provided the following information about the probabilities of the number of faulty products produced per week.

X | F(x)

0 .16

1 .35

2 .42

3 .09

4 .01

Is this a valid probability distribution? If not, why?

Is this a valid probability distribution? If not, why?

a. It is not a valid probability distribution because ∑f(x) > 1.

b. It is not a valid probability distribution because ∑f(x) < 1.

c. It is not a valid probability distribution because f(O) ≠ 0.

d. Yes, it is a valid probability distribution.

Answer: a. It is not a valid probability distribution because ∑f(x) > 1.

If a random variable can assume one of five outcomes and the distribution is uniform, what is the probability function for this random variable?

a. f(x) = 5

b. f(x) = x5

c. f(x) = 1/5x

d. f(x) = .20

Answer: d. f(x) = .20

Which of the following is not a required condition for a discrete probability function?

a. ∑f(x) = 1

b. ∑f(x) ≥ 0 for all values of x

c. ∑f(x) = 0

d. All of these choices are correct.

Answer: c. ∑f(x) = 0

The probability function for the number of people in a randomly selected vehicle is given below. What is the probability that there are less than three people in a randomly selected vehicle?

x |1 | 2 | 3 | 4

f(x)|.4|.35|.15|.1

a. .25

b. .90

c. .75

d. 1

Answer: c. .75

Which of the following could represent a discrete uniform probability function?

a. f(x) = 5 n where n is the number of values the random variable can assume

b. f(x) = 4^x

c. f(x) = 1/6

d. f(x) = 6/5

Answer: c. f(x) = 1/6

A pediatrician records the heights and ages of her patients over a one month period. The average height is recorded for each age and is an example of a:

a. continuous random variable.

b. discrete random variable.

c. None of these choices are correct.

d. complex random variable.

Answer: a. continuous random variable.

The amount of time a patient must wait to be seen at a doctor's office is an example of:

a. either a continuous or a discrete random variable, depending on the gender of the individual.

b. a continuous random variable.

c. a discrete random variable.

d. either a continuous or a discrete random variable, depending on the type of doctor's office.

Answer: b. a continuous random variable.

A continuous random variable may assume:

a. only the positive integer values in an interval.

b. only fractional values in an interval or collection of intervals.

c. only integer values in an interval or collection of intervals.

d. any value in an interval or collection of intervals.

Answer: d. any value in an interval or collection of intervals.

Which of the following is a continuous random variable?

a. The number of goals scored in a hockey game

b. The number of correct answers on a multiple choice test

c. The heights of children in a preschool

d. The number of houses for sale in a city

Answer: c. The heights of children in a preschool