Grade 11 · Math · Algebra 2

11th grade Probability distributions, expected value, and the spread of a random variable worksheet

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

Grade 11 Math Worksheet

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

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?
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?
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?
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?
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.
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.
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.
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
Tala records the class team's goals in each of 20 games. What is the mean number of goals per game?
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Table: tries = 1, 2, 3, 4, 5, 6; number of times = 4, 6, 5, 3, 1, 1 (20 in all).
Ari counts the tries each of 20 students needs to fly a kite. What is the mean number of tries per student?

11th grade Probability distributions, expected value, and the spread of a random variable worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Probability distributions, expected value and spread. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read a probability distribution from a dot plot or table and check that its chances add to 1.
I can find the expected value as the balance point, Σ x·P(x), for a theoretical or an observed distribution.
I can find the variance and standard deviation of a small distribution, and compare spreads.

Standard: S-MD.A.1 (+), S-MD.A.2 (+), S-MD.A.3 (+), S-MD.A.4 (+)

Words to know

random variable: A number that comes from a chance event, like goals in a game.

probability distribution: Every value with its chance; the chances add to 1.

expected value: The balance point: each value times its chance, added.

observed distribution: Chances from counts in real data.

variance: The weighted average of the squared gaps from the balance point.

standard deviation: The square root of the variance: a typical gap.

Common mistakes

Left out the edge value when finding the chance of "at least" or "at most" a number. Say together: at least 2 means 2 or more.

Gave a count of dots instead of a chance.

Gave the total of the chances shown instead of the missing chance. Check together that all the chances add to 1.

What to say

Ask: out of how many dots?

Questions parents ask

What is the most common mistake with probability distributions, expected value, and the spread of a random variable?

Left out the edge value when finding the chance of "at least" or "at most" a number. Say together: at least 2 means 2 or more.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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