Business Analytics I (BUAL 2600) Exam 2

The manager of the local grocery store has determined that, on average, 4customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, exactly 3 customers use the service desk?

0.1954

Suppose that historical sales records indicate that 40% of all customers who enter a discount department store make a purchase. What is the probability that two of the next three customers will make a purchase?

0.288

If A and B are independent events, P(A) = .2, and P(B) = .7, determine P(A∪B)

0.76

If A and B are independent events, P(A) = .2, and P(B) = .7, determine P(A∪B).

0.76

Sample Space of choosing 1 card out of the deck, then choosing 2 cards out of the same deck without replacing the 1st one.

1 card will have 52 (52 cards in a deck) 2 cards will have 2652 (52 * 51)

If n = 15 and p = .4, then the standard deviation of the binomial distribution is _______

1.897

If n = 15 and p = .4, then the standard deviation of thebinomial distribution is _______

1.897

Let A, B, and C be events and assume the following probabilities: P(A) = 0.2, P(B) = 0.3, P(C) = 0.5, P(A ∩ B) =0.06, P(A ∩ C) = 0, P(B ∩ C) = 0.5. Which two of the three events are mutually exclusive?

A,C

.45

An experiment has sample space S = {a, b, c, d, e}. The following table gives the probabilities for these outcomes, except P(c) is unknown. If we define the event E = {a, b, c}, what is P(E)?

Which of the following is not a discrete random variable? A) the number of times a light changes red in a 10-minute cycle B) the number of minutes required to run 1 mile C) the number of defects in a sample selected from a population of 100 products D) the number of criminals found in a five-mile radius of a neighborhood

B) the number of minutes required to run 1 mile

The Addition Rule

P (A u B) = P (A) + P (B) - P ( A ∩ B)

The General Multiplication Rule

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

If P(A) > 0 and P(B) > 0 and events A and B are independent, then ________.

P(A|B) = P(A)

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

Poisson

5/15

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

Example of Intersection

the middle of a Venn Diagram

Which of the following is not a discrete random variable?

the number of minutes required to run 1 mile

In which of the following are the two events A and B always independent?

the probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A).

Conditional probability

the probability that one event will occur given that we know that another event has occurred

Sample Space

the set of all possible outcomes

Probability of an Event

the sum of the probabilities of the sample space outcomes that corresponded with that event

Continuous Random Variables

typically found by measuring, such as heights or temperatures

Random Variables

variables whose values is numerical and is determined by the outcome of an experiment

Sample Space of 2 kids

{BB, BG, GB, GG} 4 total

Sample Space of 2 flips of a coin

{HH, HT, TT, TH} 4 total

Sample Space of 3 flips of a coin

{HHH, TTT, THT, TTH.....} 16 total

Probability Rules

• a probability must be a number between 0 and 1 • the sum of probabilities from all possible outcomes must equal 1 • if two events cannot occur simultaneously, the probability either one or the other occurs equals the sum of their probabilities • the probability that an event does not occur equals 1 minus the probability that the event does occur

Continuous Random Variable

a random variable whose values corresponded to one or more intervals of numbers on the real number line

Event

a set of one or more sample space outcomes.

Complement of an event

all possible outcomes that are not in the event

The requirement that the probability of success remains constant from trial to trial is a property of the ________ distribution.

binomial

A(n) ________ is the probability that one event will occur given that we know that another event already has occurred.

conditional probability

The Probability of a discrete random variable

discrete probability distribution

Discrete Probability Distribution Properties

each probability is between zero and one

If both A and B occur, this is an example of?

intersection

The ________ of two events A and B is the event that consists of the sample space outcomes belonging to both event A and event B.

intersection

If two events are independent, we can ________ their probabilities to determine the intersection probability

multiply

Expected Values of a Discrete Random Variable

multiply each value of the random variable by its products

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are ________.

mutually exclusive

The mean of the binomial distribution is equal to

np

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

poisson

The ________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

probability

What do you use to calculate probabilities?

probability rules

Discrete Random Variable

something that can be counted. (reps, number of people)

Union

the event if A and B (or both) occur