5-1 SmartBook Assignment: Chapter 6 (Sections 6.1 through 6.4)

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

P(X = x)

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

P(X ≤ x)

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

RANDOM

True or false: σ2 represents the variance.

TRUE

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.

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

squared deviations; probabilities

The expected value of a discrete distribution is the _____.

sum of the x values weighted by their probabilities.

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: 0 1 2 3 or more Probability: .2 .7 ____ .02 The probability that a student purchases 2 milk cartons is

0.08

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

1 (ONE)

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

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 _____.

46

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

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

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 _____.

Blank 1: .302 or 0.302

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 (round your answer to 3 decimal places).

Blank 1: .663 or 0.663

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

Blank 1: 31.46 EXPLANATION: √(100,000 x .01 x.99) = √990 =31.46

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 _____.

Blank 1: 6.066

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

Blank 1: binomial

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

Blank 1: success

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

Blank 1: upper Blank 2: lower

Which of the following are characteristics of a binomial distribution?

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

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 characteristics of a discrete uniform distribution?

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

True or false: E(X) = μ

True

Discrete random variables:

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

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

false

The symbol π in the binomial PDF

is the probability of success. is in the interval [0, 1].