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
easyTrue or false: a precise-looking number like 47.382% always means low uncertainty.
Example 2
challengeYou estimate a town's population as . A planner needs the population AT LEAST to fund a new school. Can you confidently claim the population meets the threshold?
Example 3
hardTrue or false: a more precise-looking number like automatically means lower uncertainty than a number like .
Example 4
hardA friend says 'I am 100\% sure it will snow Saturday.' Is that a useful statement about uncertainty, and why?
Example 5
easyA poll says favor a candidate with margin of error . Write the interval and decide whether we can be sure she has majority support.
Example 6
hardA student takes one measurement and records cm. After repeating more times, the average becomes cm. Explain why the uncertainty shrank.
Example 7
mediumTwo estimates of a true value: A is , B is . Which is more precise (less uncertain)?
Example 8
hardA juice bottle says ' mL .' What is the minimum amount you might receive?
Example 9
mediumWhy might a weather model give a probability instead of a yes/no answer?
Example 10
mediumIf a single estimate becomes the average of independent measurements, what generally happens to the uncertainty?
Example 11
hardTwo studies estimate the same parameter: Study A: ; Study B: . Are these results consistent or contradictory? How would you combine them?
Example 12
easyTrue or false: rolling a die has uncertainty about the outcome even though the rules are perfectly known.
Example 13
easyA pencil is measured at cm with a ruler marked in cm steps. What is a reasonable uncertainty estimate?
Example 14
easyA poll reports '52% support, margin of error 3%.' The expresses what?
Example 15
mediumReducing random sampling error to near zero with a huge sample, what type of uncertainty could still dominate?
Example 16
mediumA measurement is reported as cm. What range of true values does this allow?
Example 17
hardA target value is . Two estimates: A says , B says . Which estimate's interval contains the true value, and which is more precise?
Example 18
easyA forecast says tomorrow's high will be . What range of temperatures does that interval cover?
Example 19
mediumTwo thermometers read and . Do their uncertainty intervals overlap, and what does that mean about agreement?
Example 20
hardA timer reads s. As a percent of the measurement, how big is the uncertainty?