stats

the Binomial distribution

The Hypergeometric distribution is most similar to

Poisson probabilities

What does the following formula calculate? e−μμxx!

Binomial probabilities

What does the following formula calculate? n!x!(n−x)!n!x!n-x!pxpxqn−x

The variance of a discrete random variable, x.

What does the following formula calculate? ∑allx(x−μx)2⋅p(x)

the probabilities remain constant from trial to trial. The experiment consists of n identical trials. Each trial has only two possible outcomes: a success or a failure.

Which of the following are characteristics of a binomial experiment?

Asking randomly selected people whether or not they are on Facebook. Asking customers at a movie theatre if they bought popcorn.

Which of the following are examples of a binomial experiment?

The number of hairs on your head. The number of defective light bulbs in a sample of 5.

Which of the following are examples of discrete random variables?

The number of students who receive an "A" on their statistics exam. The number of people who vote for the Democratic candidate for governor in the next state election.

Which of the following are examples of discrete random variables?

1000

XYZ Corporation makes widgets. It is known that 1% of the widgets are defective. If XYZ manufactures 100,000 widgets, what is the mean number of defective widgets?

1.4

190 raisins are put into a mixture which is well stirred and then made into 100 cookies. Assuming the number of raisins in a cookie follows a Poisson distribution, what is the standard deviation?

mean

A synonym for Expected Value is the

continuous

A(n) ______ random variable is a random variable whose possible values can be any number in one or more intervals on the real number line.

random

A(n) ______ variable is a variable that assigns a number to each experimental outcome.

.0081

Looking at the provided binomial table, what is the probability of zero successes in four trials if the probability of a success is 0.70?

discrete

A ______ random variable is a random variable whose possible values can be counted or listed.

poisson

A _______ variable describes the number of occurrences of an event over a specified time period.

3.18

A drive-in movie theatre has kept the following records concerning the number of passengers per vehicle. What is the mean (or expected number) of passengers per vehicle?

number

A random variable is a variable that assigns a _______ to each experimental outcome.

.2640

Looking at the provided Poisson table, what is the probability of two occurrences if the mean number of occurrences is 1.7?

0 or greater

Each probability in a discrete probability distribution must be ______.

The mean and the variance.

For a Poisson random variable, which two measures are equal to each other?

true

True or false: The standard deviation of a discrete random variable x is the positive square root of the variance of x.

The probability of an event's occurrence in any interval is the same for all intervals of equal size. The number of times an event occurs in any interval is independent for nonoverlapping intervals.

Which of the following are characteristics of a Poisson random variable?

The probabilities remain constant from trial to trial. Each trial has only two possible outcomes: a success or a failure. The experiment consists of n identical trials.

Which of the following are characteristics of a binomial experiment?

Planting seeds and recording whether they germinate or not. Asking randomly selected people if they have a magazine subscription.

Which of the following are examples of a binomial experiment?

0.11

At a local dentist's office, 22% of the patients are found to have cavities. What is the probability that exactly four of the next ten patients will have a cavity?

0.36

At a local diner, 30% of the customers order the chef's special. What is the probability that exactly one of the next five customers will order the chef's special?

6.1

At a local restaurant, 20% of the customers order the chef's special. Suppose we define the binomial random variable, x, as the number of customers who order the chef's special. If the restaurant hosts 230 customers this evening, what is the standard deviation for this binomial distribution?

.15

Based on the following discrete probability distribution, what's the missed value? X p(x) 0 0.25 1 0.60 2 ______

np

For a binomial random variable X, μX is calculated by:

1.85

Hotels R Us has kept the following records concerning the number of guests in a room. Number of Guests Probability 1 0.35 2 0.50 3 0.10 4 0.05

25

If a Poisson random variable has an expected value of 25, we know the variance is equal to .

The mean, or expected value, of a discrete random variable

If we multiply each value of a discrete random variable x by its probability p(x) and then sum the resulting products, what do we call the result?

The probability that the event will occur x times in a specified interval.

If x is a Poisson random variable, then what does p(x) refer to?

The probability of obtaining x successes in n trials.

If x is a binomial random variable, then what does p(x) refer to?

The mean of x is 6 if p = 0.6 The variance of x is 2.4 if p = 0.6. The variance of x is 2.4 if p = 0.4.

Let x be a binomial random variable based on n=10 trials where the probability of success is p.Which of the following are true?

.0084

Looking at the provided Poisson table, what is the probability of five occurrences if the mean number of occurrences is 1.3?

.1115

Looking at the provided binomial table, what is the probability of three successes in four trials if the probability of a success is 0.35?

0.9097

Looking at the provided table, calculate the standard deviation of the discrete random variable, x.

0.8275

Looking at the provided table, calculate the variance of the discrete random variable, x.

{0, 1, 2, 3, 4}

Suppose X is the number of germinated seeds in a garden with 4 seeds planted. What are the possible values of X?

{1, 2}

Suppose X is the number of times a woman is selected when 3 people are randomly chosen (without replacement) from a group of 2 women and 2 men. What are the possible values of X?

0.18

The average number of cars sold by the a dealership company has a Poisson distribution with mean 2 cars per day. What is the probability that exactly 3 cars will be sold tomorrow?

.18

The mean number of homes sold by the Acme Realty Company has a Poisson distribution with mean 2 homes per day. What is the probability that exactly 3 homes will be sold tomorrow?

1

The probabilities in a discrete probability distribution must sum to

p(7)

The sentence "the probability that x takes the value 7" can be represented with the following symbol: __________.

the probability that x takes the value 7.

The symbol p(7) corresponding to a discrete random variable x represents ______.

The average of a random variable The mean of a random variable The expected value of a random variable

The symbol μx stands for which of the following? (Select all that apply)

The height of a college student. The time a caller spends waiting for a customer representative to come on the line.

Which of the following are examples of continuous random variables?

The time that it takes to fly between Chicago and New York. The time for a 20 year old male to run 100 yards.

Which of the following are examples of continuous random variables?

mean

mean np variance npq standard deviation npq√