Probability Distributions and Expected Value

Is this a probability distribution? Why or why not?

• No. The sum of p(x) is greater than 1.

• Yes. The sum of p(x) is 1 and individual probabilities are between 0 and 1.

• No. The table is missing x = 70 and x = 100.

• Yes. All of the probabilities are between 0 and 1.

Is this a probability distribution?

• No. The sum of p(x) is not equal to 1.

• Yes. The sum of p(x) is 1 AND the individual probabilities are between 0 and 1.

• Yes. All probabilities are between 0 and 1.

• No. The table is missing X = 70 and X = 100.

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

The table represents the probability of guessing correct on a 5 question true-false quiz. Find the probability of guessing at most one correct.

• 15.6%

• 3.1%

• 18.7%

• 81.3%

Which of the following is a discrete random variable.

• The amount of snow that falls in Glens Falls each November.

• The heights of basketball players in the NBA.

• The number of days that it snowed last winter.

• The time it takes high school students to run the mile.

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. What is the average number of customers that the owner can expect to make a purchase in the first hour of opening?

• 0.2

• 1.4

• 2.0

• 3.0

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 following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20
• 0.29
• 0.39
• 0.61

The following table shows the probability distribution for the number of children in each family in the town of Crossville. What is the average number of children per family in this town?

• 1.9

• 0.3

• 2.1

• 3

Given the probability model in the table below, what is P(5)?

X___50___20____5

P(X)_0.1__0.3____ ?

• 0.6

• 0.4

• 0

• 0.3

A student group sells 500 raffle tickets. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be three third prizes, each a $20 gift card. What is the expected value of a ticket?

• $3.50

• $0.42

• $0.21

• $0.50