Ch 6, Discrete Probability Distributions

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 more than 1 apartment in a weeks is?

0.331

A list of the top twenty restaurants in Chicago was released. Four of the restaurants specialize in seafood. If five of the restaurants are selected randomly from the list, the expected value of the number of restaurants specializing in seafood is

1

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

1

20% of a restaurant customer order the chief'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-.2= 46

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?

4

Which of the following criteria indicate it would be acceptable to approximate the hypergeometric with the binomial?

n/N< .05

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

√ (230 x 0.2 x 0.8) = 6.066

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

A list of the top twenty restaurant in Chicago was released. Four of the restaurants specialize in seafood. IF five of the restaurants are selected randomly from the list, the standard deviation for the number of restaurants specializing in seafood is

.7947

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

The probability that students purchased 2 mild cartons is

.08

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 exactly three apartments in a week is

.203

20% of a restaurant customer order the chief'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 in a minute is 1.7. Which is the probability that only 1 customer arrives in the next minute?

.311

Professor Stats has 40 students in her statistics class. 24 of the students are male. If she randomly selects 6 of her students at random, without replacement, the probability of selecting 4 men in the same sample is

.332

The standard deviation for the gallon of milk purchased is

.663

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≤3)

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 experienced to be

1000

Which of the following should one look when identifying a hypergeometric application?

A finite population, N A known number of success, s

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

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

A ____ random variable is the sum of repeated Bernoulli trails.

Binomial

The binomial distribution can approximate using the Poisson

By Letting λ =mπ When n is large and π is less than or equal to .05

The binomial distribution can be approximated using the Poisson

By letting λ = nπ When n is large and π is less than or equal to .05

Discrete random variables

Can have a finite or infinite number of values Have a set of distinct values Are countable

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

P(X =x)

The CDX of discrete random variable is a rule that defines

P(X ≤ x)

The acronym PDF means ____ distribution function and the acronym CDF mean ____ distribution functions

Probability Cumulative

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

Random

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 intervals that the occurrences are counted in should be the same length

Which of the following are characteristics of a binomial distribution?

Each trial is independents of the previous trial Each trial has two possible outcomes Each trial the probability of success remains the same

True or false: A Bernoulli experiment has three possible outcomes

False

True or false: E(X) = µ

True

True or false: α2 represents the variance

True

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

Greater than .5

Generally, a hypergeometric distribution will be used instead of a binomial distribution when?

Independence of the trials is uncertain There is a finite population Sampling is done without replacement

The symbol π in the binomial PDF

Is the probability of success Is the interval [0,1].

Which of the following random variables meets the criteria for a hypergeometric distribution?

Out of 50 adults, 10 who have graduate degree. A sample of 20 is taken. Define X to be the number of adults in the sample with a graduate degree

A Poisson process is used to observe the number of occurrences

Over time or in space

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

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

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

The variance of a discrete randon variable is the sum of the ____ ____ from µ weighted by the individual ____ for each x.

Squared deviations; probabilities

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

Success

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

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

The distribution of symmetric The random variable has a finite number of outcomes The probability of each value of the random variable is the same

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 people who vote the democratic candidate in the next presidential election The number of students who received an A on the statistical exam

In the formula to calculate a probability for the hypergeometric distribution, what does the denominator represent?

The number of ways a sample size of n can be selected from the population of size N

In which of the following ways are binomial distributions and hypergeometric distributions similar

They both have two possible outcomes: Success or failure They are both discrete distributions