# Confidence interval with known variance

> ML preparation item.

- Stable ID: `original-stats-ci`
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Expected time: 7 minutes
- Skills: confidence-intervals, standard-error, sampling-distributions
- Item JSON: https://mlprep.iwase.dev/data/items/original-stats-ci.json

## Problem

A sample of size $n=100$ has mean $\overline{x}=10$. The population standard deviation is known to be $\sigma=2$. Compute the two-sided $95\%$ $z$ confidence interval for the population mean using $z=1.96$, and interpret it correctly.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `original-stats-ci`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.