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.
Example 1
easyA weather model predicts tomorrow's high temperature as 72°F \pm 5°F. Explain what this uncertainty interval means and how forecasters should communicate it.
Example 2
mediumA scientist measures the speed of light and reports c = 299,792 \pm 1 km/s. Explain the difference between uncertainty and error, and why uncertainty can never be zero in measurement.
Example 3
easyA poll reports 52% support with margin of error ±3%. Express this as an uncertainty interval and determine if we can be confident the majority supports the policy.
Example 4
hardTwo studies estimate the same parameter: Study A: \hat{\theta} = 10 \pm 2; Study B: \hat{\theta} = 12 \pm 1. Are these results consistent or contradictory? How would you combine them?