Prob and Stats

The Poisson probability distribution is an example of a continuous probability distribution.

False

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is large.

False

The Poisson probability tables list the probabilities of x occurrences in a Poisson process for various values of U , the mean number of occurrences.

True

The weight of a box of candy bars is an example of a discrete random variable since there are only a specific number of bard in the box

False

If P(A) = 0.42 and P(B) = 0.38, then P(AnB) is: a. 0.80 b. 0.58 c. 0.04 d. 0.42 e. Cannot be determined from the given information.

E

All the outcomes (simple events) contained in one or the other of two random events, or possibly in both, make up: a. the events of an experiment b. the intersection of two events c. the probability space of an experiment d. the union of two events e. the complement of the other event

D

The number of defects in a random sample of 200 parts produced by a machine is binomially distributed with p = .03. Based on this information, the standard deviation of the number of defects in the sample is 5.82.

True

The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is: a. n / p b. np(1 - p) c. np d. np - 1 e. n(1 - p)

C

Which of the following correctly describes experiments? a. They are two random events, A and B, such that the probability of one event is not affected by the occurrence of the other event; therefore, P(A) = P(A|B). b. They are different events that have no outcomes in common. c. They are activities that result in one and only one of several clearly defined possible outcomes and that do not allow us to tell in advance which of these will prevail in any particular instance. d. All of the above. e. None of these.

C

In a book, 2 misprints occur per 100 pages. Using the cumulative Poisson probability table available in your text, we can determine which of the following probabilities in a book of 500 pages? a. The probability of finding between 5 and 6 misprints equals .099. b. The probability of finding at least 20 misprints equals .003. c. The probability of finding at least 24 misprints equals .1234. d. The probability of finding at least 20 misprints equals 1. e. The probability of finding at least 24misprints equals 1.

B

In the case of independent events A, B, and C, P(AnBnC) equals: a. P(A/B)*P(B/C)*P(C/A) b. P(A/B) + P(B/C) + P(C/A) c. P(A) * P(B) *P(C) d. P(A) + P(B) + P(C) e. P(A) * P(B)* P(C/A)

C

Which of the following statements is false with respect to a Poisson distribution? a. The Poisson distribution is an example of a discrete probability distribution. b. The Poisson distribution is more skewed to the right for smaller values of the parameter . c. The Poisson distribution is symmetrical when the value of the parameter is close to 5. d. The mean of the Poisson distribution is equal to the variance. e. All of these.

C

The additive rule of probability is used to compute the probability for an intersection of two or more events: namely, given two events A and B, P(AnB) = P(A) *P(B/A) and also = P(B) * P (A/B)

False

The Poisson parameter U is the mean number of occurrences of an event per unit of time or space during the Poisson process.

True

The addition law of probability theory is used to compute the probability for the occurrence of a union of two or more events; namely, given two events A and B, P (AuB) = P(A) + P(B) - P(AnB)

True

The conditional probability of event B, given that event A has occurred is defined by: .P(B/A)=P(AnB)/ P(A), P(A) /= 0

True

The Poisson probability distribution is an example of continuous probability distribution.

False

The binomial distribution is used to describe continuous random variables.

False

The binomial experiment requires that the successes and failure probabilities be constant from one trial to the next and also that these two probabilities be equal to each other.

False

If x is a binomial random variable with n = 20, and p = 0.5, then P(x = 20) = 1.0

False

The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Based on this, how many traffic accidents should be expected during a week long period? a. 15.33 b. 10.95 c. approximately 10.36 d. approximately 12.21 e. none of these

A

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, then P(x = 0) is: a. 2.5 b. 0.0821 c. 1.5811 d. 0.40 e. 1

B

If P(A) = 0.40, P(B) = 0.30 and P(AnB) = 0.12, then A and B are: a. dependent events b. independent events c. mutually exclusive events d. disjoint events e. none of these

B

If x is a discrete random variable, then x can take on only one of two possible values

False

In general, the simple events of an experiment take on values between 0 and 1.0, inclusive

False

If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to: a. -1 b. 0 c. 1 d. any value between 0 and 1 e. 0.5

B

In general, there is no difference between the simple events and the events.

False

Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

False

. The variance of a Poisson distribution, for which u is the average number of times that an event occurs in a certain period of time or space, is given by: a. u b. u^2 c.√(u) d. +1 e. U/N^2

A

A table, formula, or graph that shows all possible values x a random variable can assume, together with their associated probabilities P(x) is called: a. a discrete probability distribution b. a continuous probability distribution c. a bivariate probability distribution d. a law of total probability e. all of these

A

A useful graphical method of displaying the sample space for an experiment is: a. a tree diagram b. a box plot c. a histogram d. a scatterplot e. a barplot

A

Which of the following is an example of a binomial experiment? a. A shopping mall is interested in the income level of its customers and is taking a survey to gather information. b. A business firm introducing a new product wants to know how many purchases its clients will make each year. c. A sociologist is researching an area in an effort to determine the proportion of households with a male head of household. d. A study is concerned with the average number of hours worked by high school students. e. All of these.

C

Conditional probability is the probability that an event will occur, with no other events taken into consideration.

False

Different events that have no outcomes in common are mutually exclusive events.

False

If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.20, then the events A and B are mutually exclusive

False

If P(A) > 0, P(B) > 0, and P(A nB) = 0, then the events A and B are independent.

False

An experiment is any activity that results in one and only one of several clearly defined possible outcomes but that does not allow us to tell in advance which of these will prevail in any particular instance.

True

If P(A) = 0, P(B) = 0.4, and P(AnB) = 0, then events A and B are independent.

True

In a binomial experiment, the probability of success is the same on every trial.

True

Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.3. Then P(AuB) = 0.5.

True

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

True

If P(A) = 0.80, P(B) = 0.70 and P(AuB) = 0.90, then P(AnB) is:a. 0.60 b. 0.56 c. 0.72 d. 0.63 e. 0.5

A

The Poisson random variable is: a. a continuous random variable with infinitely many possible values b. a discrete random variable with infinitely many possible values c. a continuous random variable with finite number of possible values d. a discrete random variable with finite number of possible values e. all of these

B

The expected number of heads in 200 tosses of an unbiased coin is: a. 100 b. 50 c. 75 d. 125 e. 200

A

The mean of a Poisson random variable x, where is the average number of times that an event occurs in a certain period of time or space, is: a. u b. u^2 c.√(u) d. +1 e. U/N^2

A

The probability distribution of the number of accidents in Grand Rapids, Michigan, each day is given by x 0 1 2 3 4 5 P(x) .20 .15 .25 .15 .20 .05 This distribution is an example of: a. continuous probability distribution b. discrete probability distribution c. conditional probability distribution d. an expected value distribution e. Is not a probability distribution.

B

The set of all simple events of an experiment is called: a. a compound event b. a sample space c. a population d. a random sample e. all of these

B

The standard deviation of a Poisson distribution, for which u is the average number of times that an event occurs in a certain period of time or space, is given by: a. u b. u^2 c.√(u) d. +1 e. U/N^2

B

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or space is 1.5, then P(x = 2) is: a. 0.2231 b. 0.5020 c. 0.2510 d. 0.1116 e. 0.5

C

If P(A/B) = P(A), or P(B/A) = P(B), then events A and B are said to be: a. mutually exclusive b. disjoint c. independent d. dependent e. B contains A.

C

Which of the following clearly describes the general multiplicative rule of probability? a. It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events, A and B, P(AuB) = P(A)+ P(B) - P(AnB) . b. It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events A and B, P (AuB) = P(A)+ P(B) c. It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events, A and B, P(AnB) = P(A) * P(B/A) = P(AnB) = P(A/B) * P(B) d. It is a rule of probability theory that is used to compute the probability for an P(AnB) = P(A) * P (B) intersection of two or more events: for any two events A and B, e. All of these.

C

Which of the following cannot generate a Poisson distribution? a. The number of telephone calls received by a switchboard in a specified time period. b. The number of customers arriving at a gas station on Christmas day. c. The number of bacteria found in a cubic yard of soil. d. The number of children in a family. e. The number of accidents per day on a certain section of a highway

D

Which of the following distributions could not be used to describe the exact distribution for a continuous random variable? a. Binomial distribution b. Poisson distribution c. Hypergeometric distribution d. all of these e. none of these

D

Which of the following is a characteristic of a binomial problem? a. There are n identical trials, and all trials are independent b. Each trial has two possible outcomes which are traditionally labeled "failure" and "success" and the probability of success p is the same on each trial. c. We are interested in x, the number of successes observed during the n trials. d. All of these are characteristics of a binomial experiment. e. None of these

D

For a binomial experiment with n trials, p is the probability of success, q is the probability of failure, and x is the number of successes in n trials. Which one of the following statements is correct? a. p + q = 1 b. p(x) = 1 for x = 0, 1, . . ., n c. P(x = 0) =q^n d. p + q = 1 and p(x) = 1 for x = 0, 1, . . ., n e. all of these

E

Which of the following experiments can be modeled by the Poisson distribution? a. The number of calls received by a switchboard during a given period of time. b. The number of bacteria per small volume of fluid. c. The number of customer arrivals at a checkout counter during a given minute. d. The number of customer arrivals at a checkout counter during a given hour. e. All of these.

E

The mean of a Poisson distribution, where U is the average number of successes occurring in a specified interval, is √(U)

False

The probability that event A will not occur is 1- P(A^c)

False

Two events A and B are said to be independent if and only if P(A / B) = P(B) or P(B / A) = P(A).

False

The probability distribution for a discrete variable x is a formula, a table, or a graph providing p(x), the probability associated with each of the values of x

True

The probability distribution of a Poisson random variable provides a good model for data that represent the number of occurrences of a specified event in a given unit of time or space.

True

Two events A and B are said to mutually exclusive if P(AnB) = 0.

True