Business statistics Chapter 6

Select all that apply Which of the following are characteristics of a Poisson distribution? Each occurrence is independent of other occurrences. The number of occurrences must be an integer. The number of occurrences may be a positive or negative value. The intervals that the occurrences are counted in should be the same length.

1. the number of occurrences must be an integer 2. each occurrence is independent of other occurrences 3. the intervals that the occurrences are counted in should be the same length

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

Hotels R Us has kept the following records concerning the number of guests in a room. Number of guest/Probability 1 .35 2 .4 3 .1 4 .15 The expected number of guests in a room is ______(round answer to two decimal places).

2.05

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

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

Select all that apply Which expression(s) below would be correct for calculating the probability that no more than 2 of 4 patients has health insurance? P(X < 2) P(X ≤ 2) P(X = 2) + P(X = 3) + P(X = 4) P(X = 0) + P(X = 1) + P(X = 2)

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

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 _______ (round you answer to 3 decimal places.)

SqRt of 2300.20.8=6.066

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 value that occurs 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 customers who purchase concessions every 5 minutes, while a movie is playing at a theater. The number of landfills per county in the state of Texas. Twenty firms are randomly selected from the S&P 500 and asked whether they will increase hiring over the next year. The number of people out of 20 who prefer Pepsi-Cola to Coca-Cola in a blind test taste.

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

Choose the logical binomial random variable The number of late shipments for two different companies. The number of late shipments and missing shipments out of the next 12 sent. The number of late shipments out of the next 12 sent by one company. The number of late shipments over the next month.

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

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

binomial

A binomial distribution is skewed left when the probability of success is less than .5. greater than .5. equal to .5.

greater than .5.

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

less than .5 p < 0.5

A Poisson process is used to observe the number of occurrences when the occurrences are not independent. in a fixed number of trials. over time or in space.

over time or in space

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? 1.28 .41 .8 2

square root of .64 = .8

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

success

The expected value of the sum of two or more random variables is equal to the __________ of their individual expected values.

sum

To calculate the variance of the sum of two independent random variables the standard deviations are summed the individual variances are summed. the variances for each of the individual variances are summed together with the expected values of the variables.

the individual variances are summed.

True or false: The Poisson-Binomial Approximation was more useful before we had Excel because the calculations with large values of n were awkward.

true

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 (round your answer to three decimal places).

.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? (Round to three decimals and do not enter a percentage.)

.311

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 Number of milk cartons/Probability 0 .10 1 .20 2 .70 The standard deviation for the gallons of milk purchased is (round your answer to 3 decimal places).

.663

A company receives an average of 0.8 purchase orders per minute. The company wants to determine the probability of receiving 6 purchase orders in 5 minutes. What value should the company use for the mean to help calculate the probability?

.8*5=4

The probability of any x value of a discrete distribution is

0≤x≤1 Reason: Be careful, 0 and 1 are possible probabilities as well.

The sum of the probabilities of all x values in a discrete distribution equals 1 0<X<100 0<X<1

1

An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week is Poisson distributed, then the probability of renting no more than 1 apartment in a week is

0.331

In the binomial distribution which expression represents the probability of failure? x π n 1-π

1-π

Select all that apply Which of the following is an example of a binomial experiment? Asking customers how much they spend on an average trip to a grocery store. Asking randomly selected people if they are a member of Facebook. Determining the actual number of students who are late for class on a particular day. Ask customers at a movie theater if they spent $20 or more on concessions.

1. Ask customers at a movie theater if they spent $20 of more on concessions 2. Asking randomly selected people if they are a member of facebook

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

False. it only has two outcomes

Which of the following are characteristics of a binomial distribution?

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

True or False: E(X) = μ

True Reason: The expected value of random variable is the population mean of the distribution.

True or false: σ2 represents the variance.

True: Reason: The variance of a discrete random variable is the population variance, denoted by the symbol sigma-squared.

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

√(100,000 x .01 x.99) = √990 =31.46

Which of the following are examples of discrete random variables? Multiple select question. The time that it takes a student to finish their final exam. The height of a college student. The number of people who vote for the democratic candidate in the next presidential election. The number of students who received an "A" on their statistics exam.

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

One common way to describe a Poisson process is the model of departure times. the model of dependent events. the model of arrivals.

the model of arrivals.

In which of the following situations is it appropriate to use a Poisson process? The number of 1's, 2's, 3's, 4's, 5's, and 6's that show up in 200 rolls of a die. The number of calls arriving to a customer help line in a one hour period. The number of people out of 100 who voted in the last presidential election. The number of free throws a basketball player makes out of the next 20 attempts.

the number of calls arriving to a customer help line in a one hour period

An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Poisson distribution, then the probability of renting exactly three apartments in a week is (round your answer to 3 decimal places and do not enter a percentage).

(e^-2.3)(2.3^3) / 3! = 0.203

The following table represents the number of cartons of milk that the children at Hoover-Wood Elementary school purchase for lunch. Number of milk cartons/Probability 0 .2 1 .7 2 ? 3 or more .02 The probability that a student purchases 2 milk cartons is __________

.08 or 0.08

The probability of any x value of a discrete distribution is 0<x<1 0.1667 1 0≤x≤1

0≤x≤1

The average number of customers arriving at Jimmy's Burgers in a minute is 1.7. Which expression would one use to calculate the probability that at least 4 customers arrive in a randomly chosen minute? 1 - P(X≤4) 1 - P(X≤3) P(X > 4) P(X≤3)

1 - P(X≤3)

Select all that apply The binomial distribution can be approximated using the Poisson Multiple select question. when n is large and π is less than or equal to .05. when n is small and π is large. if n < 10 and π > .5. by letting λ = nπ.

1. λ=nπ 2. when n is large and π is less than or equal to .05