Finding Expected Values of Random Variables

In a particular game, a single card is randomly chosen from a box that contains 3 red cards, 1 green card, and 6 blue card. If a red card is selected, you win $2. If a green card is selected, you win $4. If a blue card is selected, you lose $1. Let X be the amount that you win. The expected value of X is

• $0.40

• $1.00

• $1.60

• $1.40

Let Z = the number students in Mr. Rooney's English class who arrive late on a randomly selected day. The expected value of Z is 2. Which one of the following is the best interpretation of what this means?

• We can be confident that at least 2 students will be late to Mr. Rooney's class on a randomly selected day.

• On average, the number of students who are late to Mr. Rooney's class on a randomly selected day is 2.

• There are 2 students in Mr. Rooney's class who almost always arrive late.

• 2 students never show up to school.

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is

• 5

• 15

• 25

• 50

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is

• 1.94

• 4.33

• 9.68

• 21.65

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

• 220

• 239

• 261

• 309

• 320

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

• 220

• 239

• 261

• 309

• 320

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

• 85

• 83.2

• 87.1

• 84.4

The distribution describes lotto ticket probabilities to win different amounts. What is the expected value for this lotto ticket? (Do not include a dollar symbol in answer)

Mathematical Equivalence

ON

Answer explanation

Expected Value is calculated by adding the product each paired outcome and probability

What is the expected number of orders per week?

• 44.50 orders

• 45.23 orders

• 44.61 orders

• Not here