Exercise · ZW-CENTRAL-LIMIT-THEOREM-004 · ★★☆ Intermediate
With the same data (36 variables, mean 2, variance 9), what is the variance of the sum \(S\)?
Choose one option.
Show answer
- B. \(324\)
Explanation
By independence variances add: \(36\cdot9=324\), and the standard deviation of \(S\) is 18.
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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