MathGPT.now
Continue with Google Solve free →
Search the complete library

What do you want to learn or calculate?

Quick linksAll calculatorsMath subjectsPractice questionsFormula library
← Probability & Statistics
00:00
Practice deliberately

Work through Probability & Statistics unit by unit, then test yourself under time.

Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 7 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.

Probability & Statistics coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

This page follows the Probability & Statistics syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use statistics practice questions with answers.

01

Data displays

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a data displays problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Center and spread

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a center and spread problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Probability rules

Define the experiment and population, select the correct probability model, calculate with its assumptions visible, and interpret uncertainty in context.

Goal: recognise a probability rules problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Random variables

Define the experiment and population, select the correct probability model, calculate with its assumptions visible, and interpret uncertainty in context.

Goal: recognise a random variables problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Sampling

Define the experiment and population, select the correct probability model, calculate with its assumptions visible, and interpret uncertainty in context.

Goal: recognise a sampling problem from its wording, carry out the governing method, and check that the result is reasonable.

06

Confidence intervals

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a confidence intervals problem from its wording, carry out the governing method, and check that the result is reasonable.

07

Regression

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a regression problem from its wording, carry out the governing method, and check that the result is reasonable.

Probability & Statistics questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: For the data 4, 7, 8, 11, 13, 15, 21, what is the interquartile range?

Probability & Statistics · Data displays

  1. 8
  2. 11
  3. 17
  4. 4
Show the worked answer
  1. The list has 7 values in order, so the median is the fourth value, 11.
  2. The lower half is 4, 7, 8, and its median is Q1 = 7.
  3. The upper half is 13, 15, 21, and its median is Q3 = 15.
  4. IQR = Q3 - Q1 = 15 - 7 = 8.

Answer: 8

Question 2: Find the mean of 12, 15, 9, 20, 14, then the sample standard deviation to two decimal places.

Probability & Statistics · Center and spread

  1. mean 14, standard deviation 4.06
  2. mean 14, standard deviation 3.63
  3. mean 14, standard deviation 16.50
  4. mean 15, standard deviation 4.06
Show the worked answer
  1. Add the values: 12 + 15 + 9 + 20 + 14 = 70, and 70 / 5 = 14.
  2. Subtract the mean from each value: -2, 1, -5, 6, 0.
  3. Square and add those: 4 + 1 + 25 + 36 + 0 = 66. For a sample, divide by n - 1 = 4, giving 16.5.
  4. The square root of 16.5 is 4.06.

Answer: mean 14, standard deviation 4.06

Question 3: P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.3. What is P(A or B)?

Probability & Statistics · Probability rules

  1. 0.8
  2. 1.1
  3. 0.3
  4. 0.9
Show the worked answer
  1. The addition rule is P(A or B) = P(A) + P(B) - P(A and B).
  2. The overlap is subtracted because it was counted twice.
  3. 0.6 + 0.5 = 1.1.
  4. 1.1 - 0.3 = 0.8.

Answer: 0.8

Question 4: A random variable X takes the values 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4, 0.2. What is the expected value of X?

Probability & Statistics · Random variables

  1. 1.7
  2. 1.5
  3. 2.0
  4. 0.25
Show the worked answer
  1. Multiply each value by its probability, then add the products.
  2. 0(0.1) = 0 and 1(0.3) = 0.3.
  3. 2(0.4) = 0.8 and 3(0.2) = 0.6.
  4. 0 + 0.3 + 0.8 + 0.6 = 1.7.

Answer: 1.7

Question 5: A population has a standard deviation of 15. What is the standard error of the mean for samples of size 25?

Probability & Statistics · Sampling

  1. 3
  2. 0.6
  3. 15
  4. 5
Show the worked answer
  1. The standard error is the population standard deviation divided by the square root of the sample size.
  2. The square root of 25 is 5.
  3. 15 / 5 = 3.
  4. So sample means vary about 3 units around the true mean.

Answer: 3

Question 6: A sample of 36 has a mean of 68 and the population standard deviation is 6. What is the 95% confidence interval for the mean?

Probability & Statistics · Confidence intervals

  1. (66.04, 69.96)
  2. (66.00, 70.00)
  3. (62.08, 73.92)
  4. (67.02, 68.98)
Show the worked answer
  1. The standard error is 6 divided by the square root of 36, which is 6 / 6 = 1.
  2. For 95% confidence the z value is 1.96.
  3. The margin of error is 1.96 x 1 = 1.96.
  4. 68 - 1.96 = 66.04 and 68 + 1.96 = 69.96.

Answer: (66.04, 69.96)

Question 7: A least-squares line has r = 0.8, with standard deviations of 3 for x and 6 for y. What is the slope?

Probability & Statistics · Regression

  1. 1.6
  2. 0.4
  3. 2.4
  4. 0.8
Show the worked answer
  1. The slope equals r times (standard deviation of y) divided by (standard deviation of x).
  2. 6 / 3 = 2.
  3. 0.8 x 2 = 1.6.
  4. So y rises about 1.6 units for each 1 unit rise in x.

Answer: 1.6

Question 8: A player makes 40% of free throws. In 5 attempts, what is the probability of exactly 2 makes?

Probability & Statistics · Probability rules

  1. 0.3456
  2. 0.2304
  3. 0.1600
  4. 0.4000
Show the worked answer
  1. This is a binomial setting: 5 fixed trials, each with success chance 0.4.
  2. The number of ways to choose which 2 shots go in is 5 choose 2 = 10.
  3. Each such outcome has probability 0.4^2 x 0.6^3 = 0.16 x 0.216 = 0.03456.
  4. 10 x 0.03456 = 0.3456.

Answer: 0.3456

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed Probability & Statistics questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1Data displaysFor the data 4, 7, 8, 11, 13, 15, 21, what is the interquartile range?8
2Center and spreadFind the mean of 12, 15, 9, 20, 14, then the sample standard deviation to two decimal places.mean 14, standard deviation 4.06
3Probability rulesP(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.3. What is P(A or B)?0.8
4Random variablesA random variable X takes the values 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4, 0.2. What is the expected value of X?1.7
5SamplingA population has a standard deviation of 15. What is the standard error of the mean for samples of size 25?3
6Confidence intervalsA sample of 36 has a mean of 68 and the population standard deviation is 6. What is the 95% confidence interval for the mean?(66.04, 69.96)
7RegressionA least-squares line has r = 0.8, with standard deviations of 3 for x and 6 for y. What is the slope?1.6
8Probability rulesA player makes 40% of free throws. In 5 attempts, what is the probability of exactly 2 makes?0.3456

How the generated Probability & Statistics sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this Probability & Statistics practice page

What does this page cover?

It covers all 7 Probability & Statistics units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.

When can I see correct answers and explanations?

The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.