Probability and Statistics Exam 2

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time 2.5, then P(X = 0) is

0.0821

If P(A) = 0.42 and P(B) = 0.38, then P(A ∩ B) is

Cannot be determined from the given information

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

False

If P(A) = 0.40, P(B) = 0.30 and P(A ∩ B) = 0.12, then A and B are

Independent events

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

True

If events A and B are mutually exclusive, then the probability of both events ocurring simultaneously is equal to

0

The expected number of heads in 200 tosses of an unbiased coin is

100

The probability distribution of the number of accidents in Grand Rapids, Michigan, each day is given by... This distribution is an example of

Discrete probability distribution

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 B) = 0, then the events A and B are independent.

False

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

False

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

False

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

False

Which of the following cannot generate a Poisson distribution?

The number of children in a family

If P(A/B) = P(A), or P(B/A) = P(B), then events A and B are said to be

independent

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 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

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

False

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(A ∩ B) x P(B|A) and also = P(B) x P(A|B)

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

The mean of a Poisson distribution, where is the average number of successes occurring in a specified interval is √μ.

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

True

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

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(A ∩ B)

True

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

True

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

False

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or spacce is 1.5, then P(x=2) is

0.2510

If P(A) = 0.80, P(B) = 0.70 and P(AUB) = 0.90, then P(A ∩ B) is

0.60

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?

15.33

The Poisson random variable is

A discrete random variable with infinitely many possible values

Which of the following is an example of a binomial experiment?

A sociologist is researching an area in an effort to determine the proportion of households with a male head of household

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 of the following statements is correct?

All of these

Which of the following distributions could not be used to describe the exact distribution for a continuous random variable?

All of these

Which of the following experiments can be modeled by the Poisson distribution?

All of these

Which of the following is a characteristic of a binomial problem?

All of these are characteristics of a binomial experiment

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

False

A table, formula, or graph that shows all possible values x a random variable can assume, togetherwith their associated probabilities P(x) is called

Continuous probability distribution

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 distribution is an example of a continuous probability distribution.

False

Which of the following clearly describes the general multiplicative rule of probability?

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(A ∩ B) = P(A) x P(B|A) = P(A ∩ B) = P(A|B) x P(B)

In the case of independent events A, B, and C, P(A ∩ B ∩ C) equals

P(A) x P(B) x P(C)

Which of the following statements is false with respect to a Poisson distribution?

The Poisson distribution is symmetrical when the value of the parameter μ is close to 5

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?

The probability of finding at least 20 misprints equals 0.003

All the outcomes (simple events) contained in one or the other of two random events, or possibly in both, make up

The union of two events

Which of the following correctly describes experiments?

They are activities that resilt 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 particulat instance

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(A B) = 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(A B) = 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

The set of all simple events of an experiment is called

a sample space

A useful graphical method of displaying the sample space for an experiment is

a tree diagram

The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is

np

The mean of a Poisson random variable x, where μ is the average number of times that an event occurs in a certain period of time or space, is

μ

The variance of a Poisson distribution, for which μ is the average number of times that an event occurs in a certain period of time or space is given by

μ

The standard deviation of a Poisson distribution, for which μ is the average number of times that an event occurs in a certain period of time or space, is given by

√μ