Practice Uncertainty in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Uncertainty is the state of having incomplete or imperfect information about a quantity, outcome, or process, making precise prediction impossible.

We don't know what will happen—statistics helps us reason under this condition.

Showing a random 20 of 50 problems.

Example 1

easy
True or false: a precise-looking number like 47.382% always means low uncertainty.

Example 2

challenge
You estimate a town's population as 12,400±60012{,}400 \pm 600. A planner needs the population AT LEAST 12,00012{,}000 to fund a new school. Can you confidently claim the population meets the threshold?

Example 3

hard
True or false: a more precise-looking number like 73.84%73.84\% automatically means lower uncertainty than a number like 74%74\%.

Example 4

hard
A friend says 'I am 100\% sure it will snow Saturday.' Is that a useful statement about uncertainty, and why?

Example 5

easy
A poll says 48%48\% favor a candidate with margin of error ±3%\pm 3\%. Write the interval and decide whether we can be sure she has majority support.

Example 6

hard
A student takes one measurement and records L=12.0±0.4L = 12.0 \pm 0.4 cm. After repeating 44 more times, the average becomes L=12.1±0.1L = 12.1 \pm 0.1 cm. Explain why the uncertainty shrank.

Example 7

medium
Two estimates of a true value: A is 50±250\pm 2, B is 50±850\pm 8. Which is more precise (less uncertain)?

Example 8

hard
A juice bottle says '500500 mL ±2%\pm 2\%.' What is the minimum amount you might receive?

Example 9

medium
Why might a weather model give a probability instead of a yes/no answer?

Example 10

medium
If a single estimate becomes the average of 44 independent measurements, what generally happens to the uncertainty?

Example 11

hard
Two studies estimate the same parameter: Study A: θ^=10±2\hat{\theta} = 10 \pm 2; Study B: θ^=12±1\hat{\theta} = 12 \pm 1. Are these results consistent or contradictory? How would you combine them?

Example 12

easy
True or false: rolling a die has uncertainty about the outcome even though the rules are perfectly known.

Example 13

easy
A pencil is measured at 14.614.6 cm with a ruler marked in 0.10.1 cm steps. What is a reasonable uncertainty estimate?

Example 14

easy
A poll reports '52% support, margin of error 3%.' The ±3%\pm 3\% expresses what?

Example 15

medium
Reducing random sampling error to near zero with a huge sample, what type of uncertainty could still dominate?

Example 16

medium
A measurement is reported as 20.0±0.520.0 \pm 0.5 cm. What range of true values does this allow?

Example 17

hard
A target value is 5050. Two estimates: A says 52±152 \pm 1, B says 49±349 \pm 3. Which estimate's interval contains the true value, and which is more precise?

Example 18

easy
A forecast says tomorrow's high will be 68°F±4°F68°F \pm 4°F. What range of temperatures does that interval cover?

Example 19

medium
Two thermometers read 20.1°C±0.2°C20.1°C \pm 0.2°C and 20.5°C±0.3°C20.5°C \pm 0.3°C. Do their uncertainty intervals overlap, and what does that mean about agreement?

Example 20

hard
A timer reads 2.50±0.052.50 \pm 0.05 s. As a percent of the measurement, how big is the uncertainty?