# Confidence intervals with known and unknown variance

> ML preparation item.

- Stable ID: `mit-18-05-s2022-pset11-q1`
- Area: Mathematics
- Topic: Statistics
- Origin: external
- Expected time: 14 minutes
- Skills: confidence-intervals, standard-error, sampling-distributions
- Item JSON: https://mlprep.iwase.dev/data/items/mit-18-05-s2022-pset11-q1.json

This site does not reproduce the third-party problem.

- Source: MIT 18.05 Introduction to Probability and Statistics
- Document: Problem Set 11
- Locator: Problem 1(a–c), page 1
- Official answer PDF page(s): 1
- Original problem: https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_pset11_pdf/
- Official answer: https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_pset11_sol_pdf/
- Answer status: official-solution


## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `mit-18-05-s2022-pset11-q1`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.