# Confidence interval with known variance

> ML Prep screening item.

- Stable ID: `math-stats-06-z-confidence-interval`
- Collection: screening
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Difficulty: medium
- Expected time: 3 minutes
- Skills: confidence-intervals
- Item JSON: https://mlprep.iwase.dev/item/math-stats-06-z-confidence-interval.json

## Problem

A sample of size $100$ has mean $10$. The population standard deviation is known to
be $2$. Construct the usual two-sided $95\%$ $z$-confidence interval for the population mean.


## Answer policy

The human page contains a collapsed answer. 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 `math-stats-06-z-confidence-interval`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.