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Confidence intervals worksheet for Statistics

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. For a survey percentage, 1/√n gives a quick estimate of the margin of error.

Also taught in Algebra 2, at its own level and with its own examples.

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Name

Confidence Intervals

Date Period

Find each margin of error or confidence interval.

  1. Find the margin of error or interval

    A machine fills bags of rice. A random sample of 9 bags has a mean weight of 89 ounces, and σ=9 ounces. Construct a 90% confidence interval for the population mean. Use z∗=1.645.
  2. A sample of 16 values drawn at random from a population with standard deviation 10 has mean 31. Find the margin of error of the 95% confidence interval for the mean. Use z∗=1.96.
  3. The mean score of 49 students chosen at random is 74 points, and scores on the test have standard deviation 7 points. How large is the margin of error for a 90% confidence interval? Use z∗=1.645.
  4. A gym records the workouts of 81 members chosen at random: the mean length is 65 minutes, and σ=18 minutes. Find the 95% confidence interval for the mean. Use z∗=1.96.
  5. A random sample of 9 commuters in a city has a mean commute of 52 minutes. Commute times have standard deviation 15 minutes. Find the margin of error of the 90% confidence interval for the mean. Use z∗=1.645.
  6. A delivery company times 36 randomly chosen deliveries and finds a mean of 60 minutes, with σ=18 minutes. Find the 95% confidence interval for the mean. Use z∗=1.96.
  7. A store looks at the receipts of 49 randomly chosen shoppers. They spent 69 dollars on average, and spending has standard deviation 28 dollars. How large is the margin of error for a 90% confidence interval? Use z∗=1.645.
  8. In a random sample of 16 phone batteries, the mean life is 42 hours. Battery life has standard deviation 6 hours. Find the 95% confidence interval for the mean. Use z∗=1.96.
  9. The heights of 100 randomly chosen tomato plants average 58 centimeters. Heights have standard deviation 50 centimeters. How large is the margin of error for a 95% confidence interval? Use z∗=1.96.
  10. A random sample of 100 has mean 61; the population standard deviation is 15. Construct a 90% confidence interval for the population mean. Use z∗=1.645.

  1. Estimate the margin of error

    In a random sample of 1,390 adults, 85% walk to work. Use 1n for the margin of error to give an interval for the percent of all adults who walk to work, to the nearest tenth.
  2. In a random sample of 1,600 adults, 35% favor a new park. Use 1n for the margin of error to give an interval for the percent of all adults who favor a new park, to the nearest tenth.
  3. In a random sample of 2,390 adults, 30% own a pet. Use 1n for the margin of error to give an interval for the percent of all adults who own a pet, to the nearest tenth.
  4. In a random sample of 530 adults, 29% walk to work. Use 1n for the margin of error to give an interval for the percent of all adults who walk to work, to the nearest tenth.
  5. In a random sample of 2,540 adults, 40% have a library card. Use 1n for the margin of error to give an interval for the percent of all adults who have a library card, to the nearest tenth.
  6. In a random sample of 100 adults, 61% favor a new park. Use 1n for the margin of error to give an interval for the percent of all adults who favor a new park, to the nearest tenth.
  7. In a random sample of 900 adults, 39% read the news daily. Use 1n for the margin of error to give an interval for the percent of all adults who read the news daily, to the nearest tenth.
  8. In a random sample of 760 adults, 26% have a library card. Use 1n for the margin of error to give an interval for the percent of all adults who have a library card, to the nearest tenth.
  9. In a random sample of 720 adults, 75% own a pet. Use 1n for the margin of error to give an interval for the percent of all adults who own a pet, to the nearest tenth.
  10. In a random sample of 1,540 adults, 54% read the news daily. Use 1n for the margin of error to give an interval for the percent of all adults who read the news daily, 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. Find the margin of error or interval

    A machine fills bags of rice. A random sample of 9 bags has a mean weight of 89 ounces, and σ=9 ounces. Construct a 90% confidence interval for the population mean. Use z∗=1.645.(84.065,93.935)
  2. A sample of 16 values drawn at random from a population with standard deviation 10 has mean 31. Find the margin of error of the 95% confidence interval for the mean. Use z∗=1.96.4.9
  3. The mean score of 49 students chosen at random is 74 points, and scores on the test have standard deviation 7 points. How large is the margin of error for a 90% confidence interval? Use z∗=1.645.1.645
  4. A gym records the workouts of 81 members chosen at random: the mean length is 65 minutes, and σ=18 minutes. Find the 95% confidence interval for the mean. Use z∗=1.96.(61.08,68.92)
  5. A random sample of 9 commuters in a city has a mean commute of 52 minutes. Commute times have standard deviation 15 minutes. Find the margin of error of the 90% confidence interval for the mean. Use z∗=1.645.8.225
  6. A delivery company times 36 randomly chosen deliveries and finds a mean of 60 minutes, with σ=18 minutes. Find the 95% confidence interval for the mean. Use z∗=1.96.(54.12,65.88)
  7. A store looks at the receipts of 49 randomly chosen shoppers. They spent 69 dollars on average, and spending has standard deviation 28 dollars. How large is the margin of error for a 90% confidence interval? Use z∗=1.645.6.58
  8. In a random sample of 16 phone batteries, the mean life is 42 hours. Battery life has standard deviation 6 hours. Find the 95% confidence interval for the mean. Use z∗=1.96.(39.06,44.94)
  9. The heights of 100 randomly chosen tomato plants average 58 centimeters. Heights have standard deviation 50 centimeters. How large is the margin of error for a 95% confidence interval? Use z∗=1.96.9.8
  10. A random sample of 100 has mean 61; the population standard deviation is 15. Construct a 90% confidence interval for the population mean. Use z∗=1.645.(58.5325,63.4675)

  1. Estimate the margin of error

    In a random sample of 1,390 adults, 85% walk to work. Use 1n for the margin of error to give an interval for the percent of all adults who walk to work, to the nearest tenth.(82.3%,87.7%)
  2. In a random sample of 1,600 adults, 35% favor a new park. Use 1n for the margin of error to give an interval for the percent of all adults who favor a new park, to the nearest tenth.(32.5%,37.5%)
  3. In a random sample of 2,390 adults, 30% own a pet. Use 1n for the margin of error to give an interval for the percent of all adults who own a pet, to the nearest tenth.(28.0%,32.0%)
  4. In a random sample of 530 adults, 29% walk to work. Use 1n for the margin of error to give an interval for the percent of all adults who walk to work, to the nearest tenth.(24.7%,33.3%)
  5. In a random sample of 2,540 adults, 40% have a library card. Use 1n for the margin of error to give an interval for the percent of all adults who have a library card, to the nearest tenth.(38.0%,42.0%)
  6. In a random sample of 100 adults, 61% favor a new park. Use 1n for the margin of error to give an interval for the percent of all adults who favor a new park, to the nearest tenth.(51.0%,71.0%)
  7. In a random sample of 900 adults, 39% read the news daily. Use 1n for the margin of error to give an interval for the percent of all adults who read the news daily, to the nearest tenth.(35.7%,42.3%)
  8. In a random sample of 760 adults, 26% have a library card. Use 1n for the margin of error to give an interval for the percent of all adults who have a library card, to the nearest tenth.(22.4%,29.6%)
  9. In a random sample of 720 adults, 75% own a pet. Use 1n for the margin of error to give an interval for the percent of all adults who own a pet, to the nearest tenth.(71.3%,78.7%)
  10. In a random sample of 1,540 adults, 54% read the news daily. Use 1n for the margin of error to give an interval for the percent of all adults who read the news daily, to the nearest tenth.(51.5%,56.5%)

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 store looks at the receipts of 64 randomly chosen shoppers. They spent 27 dollars on average, and spending has standard deviation 20 dollars. Find the 95% confidence interval for the mean. Use z∗=2. → (22,32)
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.

Statistics is usually taken around 11th or 12th 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.