SB 6.1-6.3

Each probability in a discrete probability distribution must be ______

0 or greater

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?

0.36

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?

6.1

XYZ Corporation makes widgets and it is known that 1% of the widgets are defective. Suppose we define the binomial random variable, x, as the number of defective widgets. If XYZ manufactures 100,000 widgets, then what is the variance for this binomial distribution?

990 Reason: This is the mean. The variance is npq = 100,000 × 0.01 × 0.99 = 990

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

number

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

p(7)

Suppose we could record the values a random variable x takes when we observe it over and over again. The mean of this population of all possible values is called

the expected value of x.

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

the probability that x takes the value 7.

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?

0.11 Why: Reason: P(x) = n!x!(n−x)!n!x!n-x! × pxpx × qn−xqn-x P(4) = 10!4!×6!10!4!×6! × 0.2240.224 × 0.7860.786 P(4) = 362880024×720362880024×720 × 0.00234256 × 0.225199601 = 0.11

The probabilities in a discrete probability distribution must sum to ______

1

Which of the following are examples 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?

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

Which of the following are characteristics of a binomial experiment?

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

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 mean, or expected value, of a discrete random variable

Which of the following are examples of discrete random variables?

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.

If x is a binomial random variable, with n trials. X defined in words is:

The number of successes out of n trials.

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

The probability of obtaining x successes in n trials.

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

The standard deviation of a discrete random variable, x.

Which of the following are examples of continuous random variables?

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

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.

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

The variance of a discrete random variable, x.

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?

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

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

True

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

continuous

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

discrete

A table or formula specifying the possible values as well as the probabilities of these values is called the ________ of the discrete random variable.

probability distribution

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

random

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?

{1, 2}