Exercise · ZW-CENTRAL-LIMIT-THEOREM-001 · ★☆☆ Basic
The \(X_i\) are independent with mean 50 and standard deviation 10. What is the standard deviation of \(\bar X_n\) if \(n=100\)?
Choose one option.
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- C. \(1\)
Explanation
\(\sigma/\sqrt n=10/10=1\). A typical error is dividing by \(n\) instead of \(\sqrt n\).
Review the concept: Central limit theorem
The central limit theorem states that the average \(\bar X_n\) of \(n\) independent, identically distributed variables \(X\), with mean \(\mu\) and deviation \(\sigma\), once standardized, resembles a normal \(N\).
\[\dfrac{\bar X_n-\mu}{\sigma/\sqrt n}\ \xrightarrow{d}\ N(0,1)\]
More practice problems: central limit theorem
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