Worksheets · Algebra 2

Algebra 2 confidence intervals worksheet

The margin of error is the critical value times the standard error: z* × σ/√n. The interval is the sample mean plus and minus that margin.

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Name

Confidence Intervals

Date Period

Find each margin of error or confidence interval.

  1. A random sample of 16 has mean 52; the population standard deviation is 8. Find the 95% confidence interval for the mean. Use z∗=2.
  2. A random sample of 2,950 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  3. A random sample of 25 has mean 68; the population standard deviation is 10. Find the 95% confidence interval for the mean. Use z∗=2.
  4. A random sample of 3,000 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  5. A random sample of 9 has mean 21; the population standard deviation is 15. Find the 95% confidence interval for the mean. Use z∗=2.
  6. A random sample of 850 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  7. A random sample of 36 has mean 15; the population standard deviation is 12. Find the margin of error for the mean. Use z∗=2.
  8. A random sample of 2,350 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  9. A random sample of 25 has mean 13; the population standard deviation is 10. Find the 95% confidence interval for the mean. Use z∗=2.
  10. A random sample of 1,850 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  11. A random sample of 100 has mean 26; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.
  12. A random sample of 1,700 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  13. A random sample of 100 has mean 68; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.
  14. A random sample of 800 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  15. A random sample of 100 has mean 36; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.
  16. A random sample of 550 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  17. A random sample of 100 has mean 20; the population standard deviation is 20. Find the margin of error for the mean. Use z∗=2.
  18. A random sample of 250 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.
  19. A random sample of 16 has mean 29; the population standard deviation is 8. Find the 95% confidence interval for the mean. Use z∗=2.
  20. A random sample of 2,200 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Confidence IntervalsAnswer keyVersion 1

Date Period

Find each margin of error or confidence interval.

  1. A random sample of 16 has mean 52; the population standard deviation is 8. Find the 95% confidence interval for the mean. Use z∗=2.(48,56)
  2. A random sample of 2,950 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±1.8%
  3. A random sample of 25 has mean 68; the population standard deviation is 10. Find the 95% confidence interval for the mean. Use z∗=2.(64,72)
  4. A random sample of 3,000 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±1.8%
  5. A random sample of 9 has mean 21; the population standard deviation is 15. Find the 95% confidence interval for the mean. Use z∗=2.(11,31)
  6. A random sample of 850 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±3.4%
  7. A random sample of 36 has mean 15; the population standard deviation is 12. Find the margin of error for the mean. Use z∗=2.4
  8. A random sample of 2,350 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±2.1%
  9. A random sample of 25 has mean 13; the population standard deviation is 10. Find the 95% confidence interval for the mean. Use z∗=2.(9,17)
  10. A random sample of 1,850 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±2.3%
  11. A random sample of 100 has mean 26; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.(22,30)
  12. A random sample of 1,700 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±2.4%
  13. A random sample of 100 has mean 68; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.(64,72)
  14. A random sample of 800 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±3.5%
  15. A random sample of 100 has mean 36; the population standard deviation is 20. Find the 95% confidence interval for the mean. Use z∗=2.(32,40)
  16. A random sample of 550 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±4.3%
  17. A random sample of 100 has mean 20; the population standard deviation is 20. Find the margin of error for the mean. Use z∗=2.4
  18. A random sample of 250 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±6.3%
  19. A random sample of 16 has mean 29; the population standard deviation is 8. Find the 95% confidence interval for the mean. Use z∗=2.(25,33)
  20. A random sample of 2,200 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth.±2.1%

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

xˉ=50, σ=12, n=36, z∗=1.96. Find the 95% interval

  1. The standard error is 12/6 = 2.
  2. The margin of error is 1.96 × 2 = 3.92.

The answer is (46.08,53.92).

Where students go wrong

Saying there is a 95% chance the mean is in this particular interval. The 95% describes the method: about 95 of every 100 intervals built this way catch the true mean.

Also called margin of error, confidence interval for a mean or z-interval.

What you can put on this worksheet

Margin of error and the interval
A random sample of 16 has mean 69; the population standard deviation is 8. Find the margin of error for the mean. Use z∗=2. → 4
Margin of error from the sample size
A random sample of 1,650 adults is surveyed. Estimate the margin of error with 1n, as a percent to the nearest tenth. → ±2.5%

Questions about these worksheets

Yes. Every confidence intervals sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the confidence intervals questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: margin of error and the interval and margin of error from the sample size. Tick as many as you want and set how many of each, or let it spread them evenly.

Saying there is a 95% chance the mean is in this particular interval. The 95% describes the method: about 95 of every 100 intervals built this way catch the true mean.