# Approximate a binomial central range

> ML Prep screening item.

- Stable ID: `math-prob-07-sum-clt`
- Collection: screening
- Area: Mathematics
- Topic: Probability
- Origin: original
- Difficulty: medium
- Expected time: 4 minutes
- Skills: sums-of-random-variables, central-limit-theorem
- Item JSON: https://mlprep.iwase.dev/item/math-prob-07-sum-clt.json

## Problem

Let $X_1,\ldots,X_{100}$ be independent $\operatorname{Bernoulli}(1/2)$ variables
and $S=\sum_iX_i$. Identify the exact distribution of $S$ and use a normal
approximation with continuity correction to estimate $P(45\le S\le55)$.


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## Tutoring contract

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