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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 is the mean of a normal distribution N(70,10) if the second parameter is the standard deviation?

Please select an answer first.

Correct answer: A

The correct answer is 70.

  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 first parameter is the center or mean.
  3. Check the probability and interpretation: The correct answer is 70.

The first parameter is the center or mean.

2. QuestionMultiple choice

What is the standard deviation in N(70,10) under this notation?

Please select an answer first.

Correct answer: B

The correct answer is 10.

  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 second parameter is specified as the standard deviation.
  3. Check the probability and interpretation: The correct answer is 10.

The second parameter is specified as the standard deviation.

3. QuestionMultiple choice

What is the z-score of x=85 for mean 70 and standard deviation 10?

Please select an answer first.

Correct answer: C

The correct answer is 1.5.

  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: z=(85-70)/10=1.5.
  3. Check the probability and interpretation: The correct answer is 1.5.

z=(85-70)/10=1.5.

4. QuestionMultiple choice

In a standard normal distribution, what are the mean and standard deviation?

Please select an answer first.

Correct answer: D

The correct answer is Mean 0 and standard deviation 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 standard normal distribution is N(0,1).
  3. Check the probability and interpretation: The correct answer is Mean 0 and standard deviation 1.

The standard normal distribution is N(0,1).

5. QuestionMultiple choice

Approximately what proportion of a normal distribution lies below the mean?

Please select an answer first.

Correct answer: A

The correct answer is 0.5.

  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: Symmetry places half the area below the mean.
  3. Check the probability and interpretation: The correct answer is 0.5.

Symmetry places half the area below the mean.

6. QuestionMultiple choice

Approximately what proportion lies within 1 standard deviation of the mean?

Please select an answer first.

Correct answer: B

The correct answer is 0.68.

  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 empirical rule gives about 68%.
  3. Check the probability and interpretation: The correct answer is 0.68.

The empirical rule gives about 68%.

7. QuestionMultiple choice

What is the shape of a standard normal curve?

Please select an answer first.

Correct answer: C

The correct answer is Symmetric and centered at 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: Standardizing preserves the normal bell shape and centers it at zero.
  3. Check the probability and interpretation: The correct answer is Symmetric and centered at 0.

Standardizing preserves the normal bell shape and centers it at zero.

8. QuestionMultiple choice

If z=-2, how many standard deviations below the mean is the value?

Please select an answer first.

Correct answer: D

The correct answer is 2.

  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 negative sign indicates below the mean and the magnitude is 2.
  3. Check the probability and interpretation: The correct answer is 2.

The negative sign indicates below the mean and the magnitude is 2.

9. QuestionMultiple choice

What does standardizing a value do?

Please select an answer first.

Correct answer: A

The correct answer is Converts it to a z-score.

  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: A z-score expresses distance from the mean in standard deviations.
  3. Check the probability and interpretation: The correct answer is Converts it to a z-score.

A z-score expresses distance from the mean in standard deviations.

10. QuestionMultiple choice

If X is normal, what kind of distribution does a linear transformation of X have?

Please select an answer first.

Correct answer: B

The correct answer is Another normal distribution.

  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: Normal distributions are preserved under linear transformations.
  3. Check the probability and interpretation: The correct answer is Another normal distribution.

Normal distributions are preserved under linear transformations.

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