Confidence intervals worksheet for Algebra 2

Algebra 2 introduces confidence intervals with two formulas: the margin of error for a mean, z* × σ/√n, and the quick estimate 1/√n for a survey percentage. Some questions stop at the margin of error; others add and subtract it to give the interval.

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

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Confidence Intervals Date Period Find each margin of error or confidence interval. Find the margin of error or interval A store looks at the receipts of 36 randomly chosen shoppers. They spent 60 dollars on average, and spending has standard deviation 24 dollars. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . The heights of 81 randomly chosen tomato plants average 88 centimeters. Heights have standard deviation 9 centimeters. Find the margin of error of the 95% confidence interval for the mean. Use $z^{} = 2$ . A park times 16 randomly chosen visitors on a trail: mean 84 minutes, with $σ = 20$ minutes. Construct a 95% confidence interval for the population mean. Use $z^{} = 2$ . A random sample of 9 commuters in a city has a mean commute of 58 minutes. Commute times have standard deviation 9 minutes. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . The mean score of 100 students chosen at random is 54 points, and scores on the test have standard deviation 25 points. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . A sample of 121 values drawn at random from a population with standard deviation 22 has mean 68. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . A gym records the workouts of 64 members chosen at random: the mean length is 35 minutes, and $σ = 16$ minutes. Find the margin of error of the 95% confidence interval for the mean. Use $z^{} = 2$ . A machine fills bags of rice. A random sample of 36 bags has a mean weight of 17 ounces, and $σ = 9$ ounces. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . A random sample of 100 has mean 87; the population standard deviation is 40. Construct a 95% confidence interval for the population mean. Use $z^{} = 2$ . A delivery company times 100 randomly chosen deliveries and finds a mean of 53 minutes, with $σ = 50$ minutes. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . Estimate the margin of error A random sample of 1,150 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 350 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 1,400 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 200 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 1,750 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 900 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 2,300 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 500 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 700 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. A random sample of 1,100 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Confidence Intervals

Date Period

Find each margin of error or confidence interval.

Find the margin of error or interval
A store looks at the receipts of 36 randomly chosen shoppers. They spent 60 dollars on average, and spending has standard deviation 24 dollars. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ .
The heights of 81 randomly chosen tomato plants average 88 centimeters. Heights have standard deviation 9 centimeters. Find the margin of error of the 95% confidence interval for the mean. Use $z^{*} = 2$ .
A park times 16 randomly chosen visitors on a trail: mean 84 minutes, with $σ = 20$ minutes. Construct a 95% confidence interval for the population mean. Use $z^{*} = 2$ .
A random sample of 9 commuters in a city has a mean commute of 58 minutes. Commute times have standard deviation 9 minutes. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ .
The mean score of 100 students chosen at random is 54 points, and scores on the test have standard deviation 25 points. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ .
A sample of 121 values drawn at random from a population with standard deviation 22 has mean 68. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ .
A gym records the workouts of 64 members chosen at random: the mean length is 35 minutes, and $σ = 16$ minutes. Find the margin of error of the 95% confidence interval for the mean. Use $z^{*} = 2$ .
A machine fills bags of rice. A random sample of 36 bags has a mean weight of 17 ounces, and $σ = 9$ ounces. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ .
A random sample of 100 has mean 87; the population standard deviation is 40. Construct a 95% confidence interval for the population mean. Use $z^{*} = 2$ .
A delivery company times 100 randomly chosen deliveries and finds a mean of 53 minutes, with $σ = 50$ minutes. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ .

Estimate the margin of error
A random sample of 1,150 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 350 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 1,400 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 200 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 1,750 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 900 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 2,300 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 500 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 700 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.
A random sample of 1,100 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth.



Sigma Prep · sigmaprep.io/worksheets Name Confidence IntervalsAnswer keyVersion 2 Date Period Find each margin of error or confidence interval. Find the margin of error or interval A store looks at the receipts of 36 randomly chosen shoppers. They spent 60 dollars on average, and spending has standard deviation 24 dollars. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . $(52, 68)$ The heights of 81 randomly chosen tomato plants average 88 centimeters. Heights have standard deviation 9 centimeters. Find the margin of error of the 95% confidence interval for the mean. Use $z^{} = 2$ . $2$ A park times 16 randomly chosen visitors on a trail: mean 84 minutes, with $σ = 20$ minutes. Construct a 95% confidence interval for the population mean. Use $z^{} = 2$ . $(74, 94)$ A random sample of 9 commuters in a city has a mean commute of 58 minutes. Commute times have standard deviation 9 minutes. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . $6$ The mean score of 100 students chosen at random is 54 points, and scores on the test have standard deviation 25 points. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . $5$ A sample of 121 values drawn at random from a population with standard deviation 22 has mean 68. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . $(64, 72)$ A gym records the workouts of 64 members chosen at random: the mean length is 35 minutes, and $σ = 16$ minutes. Find the margin of error of the 95% confidence interval for the mean. Use $z^{} = 2$ . $4$ A machine fills bags of rice. A random sample of 36 bags has a mean weight of 17 ounces, and $σ = 9$ ounces. Find the 95% confidence interval for the mean. Use $z^{} = 2$ . $(14, 20)$ A random sample of 100 has mean 87; the population standard deviation is 40. Construct a 95% confidence interval for the population mean. Use $z^{} = 2$ . $(79, 95)$ A delivery company times 100 randomly chosen deliveries and finds a mean of 53 minutes, with $σ = 50$ minutes. How large is the margin of error for a 95% confidence interval? Use $z^{} = 2$ . $10$ Estimate the margin of error A random sample of 1,150 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.9 %$ A random sample of 350 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 5.3 %$ A random sample of 1,400 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.7 %$ A random sample of 200 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 7.1 %$ A random sample of 1,750 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.4 %$ A random sample of 900 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.3 %$ A random sample of 2,300 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.1 %$ A random sample of 500 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 4.5 %$ A random sample of 700 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.8 %$ A random sample of 1,100 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.0 %$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Confidence IntervalsAnswer keyVersion 2

Date Period

Find each margin of error or confidence interval.

Find the margin of error or interval
A store looks at the receipts of 36 randomly chosen shoppers. They spent 60 dollars on average, and spending has standard deviation 24 dollars. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ . $(52, 68)$
The heights of 81 randomly chosen tomato plants average 88 centimeters. Heights have standard deviation 9 centimeters. Find the margin of error of the 95% confidence interval for the mean. Use $z^{*} = 2$ . $2$
A park times 16 randomly chosen visitors on a trail: mean 84 minutes, with $σ = 20$ minutes. Construct a 95% confidence interval for the population mean. Use $z^{*} = 2$ . $(74, 94)$
A random sample of 9 commuters in a city has a mean commute of 58 minutes. Commute times have standard deviation 9 minutes. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ . $6$
The mean score of 100 students chosen at random is 54 points, and scores on the test have standard deviation 25 points. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ . $5$
A sample of 121 values drawn at random from a population with standard deviation 22 has mean 68. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ . $(64, 72)$
A gym records the workouts of 64 members chosen at random: the mean length is 35 minutes, and $σ = 16$ minutes. Find the margin of error of the 95% confidence interval for the mean. Use $z^{*} = 2$ . $4$
A machine fills bags of rice. A random sample of 36 bags has a mean weight of 17 ounces, and $σ = 9$ ounces. Find the 95% confidence interval for the mean. Use $z^{*} = 2$ . $(14, 20)$
A random sample of 100 has mean 87; the population standard deviation is 40. Construct a 95% confidence interval for the population mean. Use $z^{*} = 2$ . $(79, 95)$
A delivery company times 100 randomly chosen deliveries and finds a mean of 53 minutes, with $σ = 50$ minutes. How large is the margin of error for a 95% confidence interval? Use $z^{*} = 2$ . $10$

Estimate the margin of error
A random sample of 1,150 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.9 %$
A random sample of 350 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 5.3 %$
A random sample of 1,400 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.7 %$
A random sample of 200 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 7.1 %$
A random sample of 1,750 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.4 %$
A random sample of 900 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.3 %$
A random sample of 2,300 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 2.1 %$
A random sample of 500 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 4.5 %$
A random sample of 700 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.8 %$
A random sample of 1,100 adults is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. $\pm 3.0 %$

How to do these

A random sample of 625 voters is surveyed. Estimate the margin of error with $\frac{1}{\sqrt{n}}$ , as a percent.

The square root of 625 is 25.
1/25 = 0.04, which is 4%.

The answer is $\pm 4 %$ .

Where students go wrong

Forgetting the square root on n. A sample of 625 gives a margin of 1/25, not 1/625; that is also why four times the sample size only halves the margin.

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 $\frac{1}{\sqrt{n}}$ , as a percent to the nearest tenth. → $\pm 2.5 %$

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.

Confidence intervals worksheet for Algebra 2

Select your difficulty

Find the margin of error or interval

Estimate the margin of error

Find the margin of error or interval

Estimate the margin of error

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these confidence intervals worksheets free?+

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