NumicornNumicornLearn, solve, progress

Probability Distributions Practice Tests

These Grade 12 Math practice tests cover discrete and continuous random variables, probability rules, expected value, variance, binomial and geometric models, normal distributions, probability density, cumulative distributions, and model interpretation.

Skills covered

  • Checking probability distributions, complements, independence, and mutually exclusive events
  • Computing expected value and variance and interpreting long-run behavior and spread
  • Recognizing binomial conditions, parameters, expected values, and variances
  • Using geometric, continuous, density, cumulative, and normal distribution ideas
  • Standardizing values with z-scores and evaluating assumptions and model limitations

How to use these practice tests

First decide whether the random variable is a count or a measurement. Then identify the distribution and parameters, check its conditions, and interpret the probability or expected value in context.

For more Grade 12 Math practice, return to the Grade 12 Math category.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

2. Test

Grade 12 Probability Distributions Practice Tests

Practice Grade 12 Math questions about discrete and continuous random variables, expected value, variance, binomial and geometric distributions, normal distributions, probability density, and sampling models.

Choose the best answer. Identify the random-variable type and distribution, check parameters and conditions, then calculate or interpret the requested probability.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Which conditions describe a binomial setting?

Please select an answer first.

Correct answer: A

The correct answer is Fixed trials, two outcomes, constant success probability, and independence.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: These four conditions define a binomial experiment.
  3. Check the probability and interpretation: The correct answer is Fixed trials, two outcomes, constant success probability, and independence.

These four conditions define a binomial experiment.

2. QuestionMultiple choice

For a binomial variable X with n trials and success probability p, what is E(X)?

Please select an answer first.

Correct answer: B

The correct answer is np.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: The expected number of successes is n times the success probability.
  3. Check the probability and interpretation: The correct answer is np.

The expected number of successes is n times the success probability.

3. QuestionMultiple choice

For n=10 and p=0.3, what is E(X)?

Please select an answer first.

Correct answer: C

The correct answer is 3.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Use E(X)=np=10(0.3)=3.
  3. Check the probability and interpretation: The correct answer is 3.

Use E(X)=np=10(0.3)=3.

4. QuestionMultiple choice

For a binomial variable with n=20 and p=0.25, what is the variance?

Please select an answer first.

Correct answer: D

The correct answer is 3.75.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Variance is np(1-p)=20(0.25)(0.75)=3.75.
  3. Check the probability and interpretation: The correct answer is 3.75.

Variance is np(1-p)=20(0.25)(0.75)=3.75.

5. QuestionMultiple choice

What does X=exactly 2 successes mean in a binomial model?

Please select an answer first.

Correct answer: A

The correct answer is Two successes in all n trials.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Exactly specifies the count equal to 2.
  3. Check the probability and interpretation: The correct answer is Two successes in all n trials.

Exactly specifies the count equal to 2.

6. QuestionMultiple choice

What does a binomial coefficient (nk)\binom{n}{k} count?

Please select an answer first.

Correct answer: B

The correct answer is The ways to place k successes among n trials.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: The coefficient counts which trial positions contain successes.
  3. Check the probability and interpretation: The correct answer is The ways to place k successes among n trials.

The coefficient counts which trial positions contain successes.

7. QuestionMultiple choice

What is the probability of success on a single Bernoulli trial?

Please select an answer first.

Correct answer: C

The correct answer is p.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: The binomial parameter p is the constant success probability.
  3. Check the probability and interpretation: The correct answer is p.

The binomial parameter p is the constant success probability.

8. QuestionMultiple choice

What is the probability of failure on a Bernoulli trial?

Please select an answer first.

Correct answer: D

The correct answer is 1-p.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Success and failure are complementary outcomes.
  3. Check the probability and interpretation: The correct answer is 1-p.

Success and failure are complementary outcomes.

9. QuestionMultiple choice

What is a Bernoulli random variable?

Please select an answer first.

Correct answer: A

The correct answer is A variable with one trial and two outcomes.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Bernoulli variables record success or failure for one trial.
  3. Check the probability and interpretation: The correct answer is A variable with one trial and two outcomes.

Bernoulli variables record success or failure for one trial.

10. QuestionMultiple choice

If trials are not independent, can the ordinary binomial formula be used directly?

Please select an answer first.

Correct answer: B

The correct answer is No.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Independence is one of the required binomial conditions.
  3. Check the probability and interpretation: The correct answer is No.

Independence is one of the required binomial conditions.

Previous testNext test