Discrete Random Variables (College Board AP® Statistics)

At the end of a level in a video game, a player can score 0, 10, 50, or 100 points. Let the random variable represent the number of points scored by a player at the end of a level. The expected value of is 15.5 points. What is the meaning of the expected value in this context?

Sun and Jin sit next to each other on a flight. There is a 60 percent chance that Sun will fall asleep during the flight. If Sun falls asleep, there is a 70 percent chance that Jin will also fall asleep. If Sun does not fall asleep, there is a 20 percent chance that Jin will fall asleep. Let be the number of them that fall asleep during the flight.

Which of the following tables shows the probability distribution of ?

A college entrance exam contains multiple-choice questions and is designed to prevent students from choosing answers at random. For each correct answer, a student scores ten points. For each question left unanswered, a student scored three points. For each incorrect answer, a student scores zero points. Each question has seven choices. What is the minimum number of answer choices a student must eliminate on each question before guessing becomes a strategic advantage?

Dinah's Diner is famous for selling triple burgers. The triple burger consists of three beef patties, two slices of bacon, and one toasted bread bun. The mean and standard deviation for each distribution are shown in the table below. The weights of the items are assumed to be independent.

Let the random variable represent the total weight of the triple burger. Which of the following is closest to the standard deviation of ?

A bag contains a large number of tokens. Each token has a number written on it. Let represent the number written on a token when that token is selected at random from the bag. The expected value of is 8.5, and the standard deviation is approximately 3.14.

Mark selects a token at random, records the number, and returns the token to the bag. Mark then selects another token at random and subtracts the number written on the second token from the number written on the first token. Which of the following values is closest to the standard deviation of Mark's answer?