Track 7 · Estimation and Confidence Intervals · Lesson 3 of 10
Interval for a mean with known σ
Find z critical values and build and interpret a z confidence interval for a mean when the population standard deviation is known.
A bottling line has run for years and its fill weights are known to vary with a standard deviation of 4 g. After a maintenance visit, the engineer weighs 25 bottles. Has the mean fill moved away from the 500 g target? A z interval answers that in one line.
When the population standard deviation is known, the standard error of the sample mean is exactly . If the population is normal — or is large enough for the central limit theorem — then is (approximately) normal, and the interval follows directly.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Find two-sided z critical values and explain why α is halved
- Build a z interval for a mean when σ is genuinely known
- Recognise when σ is not really known and the t interval is needed
- Report a z interval in context without misreading the 95%