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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.

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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

What does a geometric random variable count?

Please select an answer first.

Correct answer: A

The correct answer is The trial number of the first success.

  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: Geometric models repeat trials until the first success.
  3. Check the probability and interpretation: The correct answer is The trial number of the first success.

Geometric models repeat trials until the first success.

2. QuestionMultiple choice

For a geometric model with success probability p, what is the expected trial number?

Please select an answer first.

Correct answer: B

The correct answer is 1p\frac{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: The geometric mean waiting time is 1/p.
  3. Check the probability and interpretation: The correct answer is 1p\frac{1}{p}.

The geometric mean waiting time is 1/p.

3. QuestionMultiple choice

If p=0.2, what is the expected trial number for the first success?

Please select an answer first.

Correct answer: C

The correct answer is 5.

  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: Compute 1/p=1/0.2=5.
  3. Check the probability and interpretation: The correct answer is 5.

Compute 1/p=1/0.2=5.

4. QuestionMultiple choice

What is the probability of no success in the first k trials of a geometric model?

Please select an answer first.

Correct answer: D

The correct answer is (1−p)k(1-p)^k.

  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: All k trials must be failures.
  3. Check the probability and interpretation: The correct answer is (1−p)k(1-p)^k.

All k trials must be failures.

5. QuestionMultiple choice

What property does the geometric distribution have?

Please select an answer first.

Correct answer: A

The correct answer is Memorylessness.

  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 chance of waiting additional trials does not depend on previous failures.
  3. Check the probability and interpretation: The correct answer is Memorylessness.

The chance of waiting additional trials does not depend on previous failures.

6. QuestionMultiple choice

What is a continuous random variable?

Please select an answer first.

Correct answer: B

The correct answer is A variable that can take values across an interval.

  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: Measurements such as time and height can take any value in a range.
  3. Check the probability and interpretation: The correct answer is A variable that can take values across an interval.

Measurements such as time and height can take any value in a range.

7. QuestionMultiple choice

For a continuous random variable, what is P(X=a) for one exact value a?

Please select an answer first.

Correct answer: C

The correct answer is Usually 0.

  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: Probability is represented by area, and a single point has zero width.
  3. Check the probability and interpretation: The correct answer is Usually 0.

Probability is represented by area, and a single point has zero width.

8. QuestionMultiple choice

What must the area under a probability density curve equal?

Please select an answer first.

Correct answer: D

The correct answer is 1.

  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 total probability over all possible values is 1.
  3. Check the probability and interpretation: The correct answer is 1.

The total probability over all possible values is 1.

9. QuestionMultiple choice

What does a cumulative distribution function give?

Please select an answer first.

Correct answer: A

The correct answer is P(X≤x).

  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 CDF accumulates probability up to and including x.
  3. Check the probability and interpretation: The correct answer is P(X≤x).

The CDF accumulates probability up to and including x.

10. QuestionMultiple choice

For a continuous variable, P(a

Please select an answer first.

Correct answer: B

The correct answer is Area under the density from a to b.

  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: Probability is the area over the interval.
  3. Check the probability and interpretation: The correct answer is Area under the density from a to b.

Probability is the area over the interval.

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