MBA Survey Quantitative Business Analysis CH 5 & 6

The sportsbook at the High Roller Casino put the odds of a certain baseball team to win the World Series at 1:25 (1 to 25). Based on those odds, what is the probability that this baseball team will win the World Series?

.0385 Reason: 1/(1+25) = .0385

The probability of patrons at O'Shannon's Restaurant going to the bar area is .3. The probability of ordering an appetizer, given the patron has gone to the bar is .5. The probability of ordering an appetizer, given the patron does not go to the bar is .2. The probability of a patron ordering an appetizer is

.29

20% of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special is

.302

The average number of customers arriving at Jimmy's Burgers is 1.7 per minute. What is the probability that only 1 customer arrives in the next minute?

.311

The probability of a customer ordering popcorn at the movie theater is .4. The probability of a customer ordering a drink at the movie theater is .65. The probability of a customer ordering popcorn and a drink is .3. If a customer has already ordered a drink, what is the probability the customer will order popcorn?

.46 P(A given B)= P(A and B)/ P(B)P(A given B) = .3/.65P(A given B) = 0.46

A grocery store placed gallons of milk on special but limited purchases to a maximum of two gallons. The table below summarizes the milk purchases. Gallons of milk 0 1 2 Probability .10 .20 .70 The standard deviation for the gallons of milk purchased is

.663

Corky and Lori process purchase orders for Acme Inc. Lori processes 60% of the purchase orders; Corky processes 40% of the purchase orders. 5% of Lori's purchase orders have errors and 2.5% of Corky's purchase orders have errors. A purchase order has an error; the probability that Lori processed the erroneous purchase order is

.75

A company receives an average of .64 purchase orders per minute. Assuming a Poisson distribution for the number of purchase orders per minute, what is the standard deviation for this distribution?

.8 square root of .64 = .8

82% of companies ship their products by truck. 47% of companies ship their product by rail. 40% of companies ship by truck and rail. What is the probability that a company ships by truck or rail?

.89

If two events are mutually exclusive then the probability of their intersection is

0

P(A) = .45 and P(B) = .2. A and B are mutually exclusive. P(A|B) =

0 because they are mutually exclusive

In order to make sure Sam gets to his final exam on time he sets 3 alarm clocks that work independently of each other. Assume the probability of any one of the alarms working is equal to .98. What is the probability that Sam is late to his final exam?

0.000008

A manufacturer of liquid laundry detergent has a .02 probability that the detergent bottles will be improperly filled. (Either too much or too little detergent.) There is a .03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the label are independent, then the probability of a bottle being filled improperly and having an improperly affixed label is

0.02 * 0.03=0.0006

The probability of Anthony being on time for work is 0.9. The probability that Anthony will take the train to work is 0.8. The probability that Anthony will be on time for work if he took the train is 0.95. The probability that Anthony is on time for work and took the train is

0.76 0.95 x 0.8 = 0.76

The probability of any x value of a discrete distribution is

0≤x≤1

The sum of the probabilities of all the outcomes in the sample space is

1

The sum of the probabilities of all x values in a discrete distribution equals

1

XYZ Corp. has filled 100,000 purchase orders during its existence. 1,100 of the purchase orders have had errors. Using an empirical probability, the probability of the next purchase order having an error is

1,100/100,000=.011

In the binomial distribution which expression represents the probability of failure?

1-π

XYZ Corp. makes widgets. 1% of the widgets are defective. XYZ manufactures 100,000 widgets, the number of defective widgets is expected to be

1000 100,000*0.01=1000

The probability of randomly selecting a "spade" from a deck of cards is

13/52= 0.25

Hotels R Us has kept the following records concerning the number of guests in a room. Number of Guests 1 2 3 4 Probability .35 .4 .1 .15 The expected number of guests in a room is

2.05

Mike is placing a bet on an upcoming horse race in which 7 horses are running. Mike places a trifecta bet that wins only if he correctly picks the first, second, and third place horses in order. There are _____ possible outcomes for the first 3 horses in the correct order.

210

A restaurant manager has 10 wait staff on duty but business has slowed down for the night and she needs to let 4 of the staff go home. How many different ways could she choose which 4 get to leave early?

210 Reason: 10!/(4! x 6!) = 210

20% of a restaurant's customers order the chef's special. 230 customers are anticipated to dine tonight at the restaurant. The expected number of chef's specials that will be ordered tonight is

230*0.2=46

A festival has become so popular that it must limit the number of tickets it issues. People who hope to attend the festival send in a request for tickets, and requests are filled by random selection. Only 21% of the ticket requests are fulfilled. What are the odds of not receiving a ticket for a random applicant?

3.76 to 1 Reason: (1−.21)/.21 = 3.76

XYZ Corp. makes widgets. 1% of the widgets are defective. XYZ manufactures 100,000 widgets. The standard deviation for this binomial distribution is

31.46 EXPLANATION: √(100,000 x .01 x.99) = √990 =31.46

Students who take the College Prep English Course the summer before entering college have a .84 probability of achieving a "B" or better in their freshman English class at college. The odds a student taking the Prep Course will receive a "B" or better in the freshman English class are

5.25 to 1 .84/(1−.84) = 5.25

G. Amitri is the coach of the high school mathletes team. There are 8 mathletes, but only 5 may represent the school at the upcoming math tournament. How many ways can G. Amitri randomly choose 5 mathletes from the 8 eligible mathletes?

56 Reason: n!/(n−x)!(x!)=8!/(8−5)!(5!)=56

20% of a restaurants customers order the chef's special. 230 customers are anticipated to dine at the restaurant tonight. The standard deviation for this binomial distribution is

6.066 SqRt of 2300.20.8=6.066

The odds against a horse winning a race were set at 7 to 1. The probability of that horse winning the race is

7+1=81/8 = .125

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

Ask customers at a movie theater if they spent $20 or more on concessions. Asking randomly selected people if they are a member of Facebook.

When determining P(B|A) knowing only P(A|B) and P(A|B'), _____ Theorem can be very helpful.

Bayes

Which theorem provides a method for revising probabilities to reflect new information?

Bayes' Theorem

A probability that can be deduced through logical reasoning before an experiment is performed is what type of probability?

Classical

Which of the following are characteristics of a Poisson distribution?

Each occurrence is independent of other occurrences. The intervals that the occurrences are counted in should be the same length. The number of occurrences must be an integer.

Which of the following are characteristics of a binomial distribution?

Each trial is independent of the previous trial. For each trial the probability of success remains the same. Each trial has only two possible outcomes.

_____ data is collected through observation.

Empirical

Consider rolling two dice. Which of the following describe two events that are collectively exhaustive?

Event 1: Rolling an even number. Event 2: Rolling an odd number. Event 1: A value of 7 or more. Event 2: A value of 6 or less. Event 1: A value of 6 or more. Event 2: A value of 8 or less.

True or false: A Bernoulli experiment has three possible outcomes.

False

True or false: The probability of winning a lottery is .0000000012. The Law of Large Numbers says that because this probability is so small, no one should ever win a lottery

False

True or false: Tree diagrams are rarely used in business planning.

False

True or false: 0! = 0

False Reason: 0! is defined as 1, not 0.

True or false: Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A ∪ B = {2, 3}

False Reason: This is the intersection, not the union.

The multiplication rule is used to calculate what type of probability?

Joint

An important theorem in probability states that as the number of trials increase, an empirical probability will approach the theoretical probability. This theorem is called the

Law of large numbers

Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% chance that he will attend Northern University. The probability that Kareem will attend either State or Northern is

P (A or B) = P(A) + P(B) P (A or B) = .55 + .33 = .88

Match the phrase with the correct compound probability. P(X > 3) P(X ≥ 3) P(X ≤ 3) P(X < 3)

P (X > 3) = More than 3 P (X ≥ 3) = at least 3 P (X ≤ 3)= no more than 3 P (X < 3) = less than 3

If the events A and B are independent and P(A) = .4 and P(A and B) = .2 then P(B) =

P(A and B)= P(A)*P(B).2 = .4*P(B)divide .4 from both sides .5 = P(B)

Given P(A) = .4, P(B) = .6, and P(A and B) = .2, calculate the conditional probability of A given B.

P(A given B) = P(A and B)/ P(B)P(A given B) = .2/.6P(A given B) = .33333....

Which expression(s) below would be correct for calculating the probability that no more than 2 of 4 patients has health insurance?

P(X = 0) + P(X = 1) + P(X = 2) P(X ≤ 2)

The CDF of a discrete random variable is a rule that defines

P(X ≤ x)

The acronym PDF means _____ distribution function and the acronym CDF means _____ distribution function.

Probability;Cumulative

The probability of a customer ordering popcorn at the movie theater is .4. The probability of a customer ordering a drink at the movie theater is .65. The probability of a customer ordering popcorn and a drink is .3. If a customer has already ordered popcorn, what is the probability the customer will order a drink?

Reason: .3/.4 = 0.75

If an event is getting a letter grade of A in your statistics class, what is the complement of receiving an A?

Receiving any grade except an A.

Which of the following events are mutually exclusive?

Rolling an odd number and an even number on the same roll of a die. Being on time and being late for an appointment.

Which of the following experiments is likely to produce a uniform discrete distribution?

The answer selected on a multiple choice question that has four choices by a student who did not study. The values that occur from repeated spins of a roulette wheel at a casino.

In which of the following situations is it appropriate to use a Poisson process?

The number of landfills per county in the state of Texas. The number of customers who purchase concessions every 5 minutes, while a movie is playing at a theater.

Choose the logical binomial random variable.

The number of late shipments out of the next 12 sent by one company.

Which of the following are examples of discrete random variables?

The number of students who received an "A" on their statistics exam. The number of people who vote for the democratic candidate in the next presidential election.

Which of the following are examples of conditional probabilities?

The probability of Angel going to the movie, given that Derrick is going to the movie. If Neil has already purchased groceries, then the probability of Colleen purchasing groceries.

Which of the following are characteristics of a discrete uniform distribution?

The random variable has a finite number of outcomes. The mean is equal to the sum of the lower and upper limits divided by 2. The probability of each value of the random variable is the same.

Binary events are those that

are collectively exhaustive are mutually exclusive

A _____ random variable is the sum of repeated Bernoulli trials.

binomial

Discrete random variables

can have a finite or infinite number of values. are countable. have a set of distinct values.

The _____ approach to assigning probability is often used before we actually observe an experiment and often assumes each outcome is equally likely.

classical

The _____ formula is used to determine the number of different ways to arrange a group of x objects from a total of n objects and the order of the objects is irrelevant.

combination

For any given event, the sum of the probability of that event and the probability of its _____ must equal one

complement

A tree diagram has _____ probabilities at the terminal end of each branch.

conditional

The probability of Murali going to the coffee shop is 0.7. The probability of Connie going to the coffee shop is 0.4. If Murali goes to the coffee shop, the probability of Connie going to the coffee shop is 0.48. The events Murali going to the coffee shop and Connie going to the coffee shop are

dependent.

Assume P(A) = .3 and P(B) = .4. If the P(A or B) = .7 we can say that A and B are

disjoint mutually exclusive

Probabilities that are estimated from observed frequencies are called

empirical

The three ways of assigning probability are

empirical classical subjective

Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of

event B.

Events that cannot both occur at the same time are mutually _____ events

exclusive

The _____ rule is useful for counting the possible arrangements of any n items

factorial

A binomial distribution is skewed left when the probability of success is

greater than .5.

The probability that a customer will purchase a product is 0.15. The probability that a customer is a male is 0.5. The probability that a customer is a male and will purchase a product is 0.075. The events purchasing a product and being a male are

independent

The probability of State College winning a football game is .6. The probability of University of State winning a football game is .65. Given that State College has won its football game, the probability of University of State winning its game is .65. The teams are not playing each other. The events State College winning and University of State winning are

independent.

The _____ of two events A and B contains only those outcomes that are in both A and B

intersection

Define event A = {1, 2, 3, 4} and event B = {6, 7, 8}. A ∩ B =

null set

The _____ formula is used to determine the number of ways to arrange x objects from a group of n objects where the order of the objects matters.

permutation

A _____ variable assigns numerical values to the outcomes of a random experiment.

random

A trial, or process, that produces several possible outcomes that cannot be known in advance is called an/a

random experiment

A contingency table is sometimes called an r x c table where r stands for number of _____ and c stands for number of _____

rows; columns

The variance of a discrete random variable is the sum of the ______ _______ from μ weighted by the individual ___________ for each x.

squared deviations; probabilities

A probability assigned by a person that is based on that person's judgment or experiences is a _____ probability

subjective

A softball coach believes that Laurie has a .3 probability of getting a hit against a left-handed pitcher that Laurie has never batted against before. The .3 probability that the coach has assigned is what type of probability?

subjective

The mean of a Bernoulli distribution is π, called the probability of

success

The expected value of a discrete distribution is the

sum of the x values weighted by their probabilities.

A binomial distribution is _____ when π = .50.

symmetrical

A conditional probability is calculated by dividing the probability of the intersection of two events by the probability of

the given event.

Contingency tables are useful to analyze

the results of a survey. relative frequencies

The addition rule is used to calculate

the union of two events

Bayes' _________ is used to revise probabilities when one has new ______

theorem, information

To calculate a joint probability from a contingency table, the frequency of each cell is divided by the

total number of outcomes in the sample space

A prior probability for event A is the _____ probability whereas the posterior probability of event A is the _____ probability.

unconditional;conditional

Random variables are represented by _____-case letters, while particular values of random variables are represented by _____-case letters.

upper;lower

Probability values range from

zero, one

Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A ∪ B =

{1, 2, 3, 4, 6, 7}