Lesson 6.2 Analyze Discrete Random Variables

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

• 85

• 83.2

• 87.1

• 84.4

Choose an American household at random. What is the expected number of cars for that household?

• 1.75
• 1.84
• 2.00
• 2.50

Which of the following best describes how to calculate expected value?

• Add each possible outcome together, and multiply the sum by the probability of the least likely outcome.

• Multiply each possible outcome by its probability, and add each product together.

• Multiply each possible outcome by itself, and add each product together.

• Add each probability together, and multiply it by the sum of each possible outcome.

Which of the following expressions correctly shows an expected value calculation for the probability distribution below?

Ana is a dedicated Skee Ball player who always rolls for the 50-point slot. The histogram of the probability distribution of Ana’s score 𝑋 on a randomly selected roll of the ball is shown here. What is the shape of this histogram?

• The shape of the probability histogram is skewed to the right with a single peak at a score of 10 points.

• The shape of the probability histogram is approximately Normal with a single peak at a score of 10 points.

• The shape of the probability histogram is fairly uniform with a single peak at a score of 10 points.

• The shape of the probability histogram is skewed to the left with a single peak at a score of 10 points.

Choose an American household at random and let the random variable 𝑋 be the number of cars (including SUVs and light trucks) they own. The standard deviation of 𝑋 is 𝜎𝑥 = 1.08. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The number of cars would be at most 1.08 from the mean.

• The number of cars would be within 1.08 from the mean about 68% of the time.

• The mean number of cars would be about 1.08.

• The number of cars would typically be about 1.08 from the mean.

The table represents the probability of guessing correct on a 5 question true-false quiz. Find the mean and the standard deviation.

• μ = .4; σ = 7.5

• μ = 2.5; σ = 1.1

• μ = 3; σ = 1.3

• μ = .1; σ = 0

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

The number of students in a room.

• Discrete

• Continuous

The table represents the probability of guessing correct on a 5 question true-false quiz.  Find the probability for at least 4 questions correct.

• .03125
• .15625
• .3125
• .1875