Statistics Probability Distributions

It is a variable whose values depend on outcomes of a random phenomenon.

• Random Variable

• Discrete Variable

• Continuous Variable

• Independent Variable

Is the following a probability distribution?

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.

• No, all probabilities are not be between 0 and 1 inclusive

• No, the sum of all the probabilities is not 1.

• Yes, because the distribution is symmetric

Is the following a probability distribution?

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.

• No, all probabilities are not be between 0 and 1 inclusive

• No, the sum of all the probabilities is not 1.

• Yes, because the distribution is symmetric

A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the probability distribution shown. What is the probability that a randomly chosen household has at least two cars?

• 0.20

• 0.29

• 0.39

• 0.61

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14

• 4.67

• 5

• 7.5

The following table represents the probability distribution X, the employment status of adults in a city. What is the probability that the adults isn't retired?

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household?

HINT: It may be helpful to make a probability distribution table.

• 2.00

• 2.13

• 1.97

• 1.27

The following table represents the probability distribution X, the employment status of adults in a city. What is the probability that the adults isn't retired?

What is the mean of the probability distribution?

• 4.13

• 5.18

• 5.54

• 6.08

What is the variance of the distribution?

• 8.04

• 8.40

• 9.50

• 9.05