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 = 0.5, 0.4, 0.2, -0.1
   • P = 0.3, 0.4, 0.2, 0.1
   • P = 0.4, 0.3, 0.3, 0.1
   • P = 0.6, 1.2, -0.4, -0.4
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, 0.35, 0.15
   • P = 0.45, -0.05, 0.35, 0.25
   • P = 0.25, 0.25, 0.25, 0.35
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 = -0.2, 0.6, 0.4, 0.2
   • P = 0.15, 0.45, 0.3, 0.2
   • P = 1, 1, 1, 1
   • P = 0.05, 0.45, 0.3, 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, 0.6, 0.25, 0.05
   • P = 0.1, 0.7, 0.25, -0.05
   • P = 0.25, 0.25, 0.25, 0.2
   • P = 0.1, 0.5, 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. 10.

    Zee counts the people in each of 50 cars at a school drop-off. What is the mean number of people per car?

    1.92