Probability Distributions and Expected Value

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 in this town?

• 1.9

• 0.3

• 2.1

• 3

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

Is this a probability distribution?

• No

• Yes

• Discrete
• Continuous

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.

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

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

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

The following table shows the probability distribution for the number of children in each family in the town of Crossville. Interpret P(X < 2).

• The probability that a randomly selected family in Crossville has less than two children is 40%.

• The probability that a randomly selected family in Crossville has less than two children is 70%.

• The probability that a randomly selected family in Crossville has more than two children is 30%.

• The probability that a randomly selected family in Crossville has less than two children is 3%.