Probability distributions, expected value, and the spread of a random variable

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Bo's table gives the distribution of correct answers when guessing on 2 questions with 4 choices each. How many correct answers should Bo expect?

   0.5
2. 2.

   Esme's table gives the distribution of the number of people in each car arriving at a school concert. What is the expected number of people per car?

   1.95
3. 3.

   Table: x = 0, 1, 2, 3; P(x) = 0.3, 0.35, 0.25, 0.1. Jun's table gives the distribution of the number of goals the class team scores in a game. What is the expected number of goals?

   1.15
4. 4.

   Table: x = 10, 20, 30, 50; P(x) = 0.4, 0.3, 0.2, 0.1. Kira's table gives the distribution of the points a team earns for one answer in a class quiz game. What is the expected number of points?

   21
5. 5.

   Luz writes four lists of chances for the number of rainy days in a 3-day class trip, for x = 0, 1, 2, 3. Which list can be a probability distribution?

   • P = 0.3, 0.4, 0.2, 0.1
   • P = 0.6, 1.2, -0.4, -0.4
   • P = 0.4, 0.3, 0.3, 0.1
   • P = 0.5, 0.4, 0.2, -0.1
6. 6.

   Milo writes four lists of chances for the number of puzzles a club solves in an hour, for x = 0, 1, 2, 3. Which list can be a probability distribution?

   • P = 0.2, 0.3, 0.25, 0.15
   • P = 0.25, 0.25, 0.25, 0.35
   • P = 0.25, 0.25, 0.35, 0.15
   • P = 0.45, -0.05, 0.35, 0.25
7. 7.

   Noah writes four lists of chances for the number of kites in the air at the park, for x = 0, 1, 2, 3. Which list can be a probability distribution?

   • P = 0.15, 0.45, 0.3, 0.2
   • P = 1, 1, 1, 1
   • P = 0.05, 0.45, 0.3, 0.2
   • P = -0.2, 0.6, 0.4, 0.2
8. 8.

   Pia writes four lists of chances for the number of shells found on a beach walk, for x = 0, 1, 2, 3. Which list can be a probability distribution?

   • P = 0.1, 0.5, 0.25, 0.05
   • P = 0.25, 0.25, 0.25, 0.2
   • P = 0.1, 0.6, 0.25, 0.05
   • P = 0.1, 0.7, 0.25, -0.05
9. 9.

   Tala records the class team's goals in each of 20 games. What is the mean number of goals per game?

   1.25

10. Read this first

    Use this

    Table: tries = 1, 2, 3, 4, 5, 6; number of times = 4, 6, 5, 3, 1, 1 (20 in all).

11. 10.

    Ari counts the tries each of 20 students needs to fly a kite. What is the mean number of tries per student?

    2.7