Exercise · ZW-CENTRAL-LIMIT-THEOREM-006 · ★☆☆ Basic
With \(\mu=50\), \(\sigma=8\) and \(n=64\), what is \(Z=\dfrac{\bar X_n-\mu}{\sigma/\sqrt n}\) if \(\bar X_n=52\)?
Choose one option.
Show answer
- A. \(2\)
Explanation
The standard error is \(8/8=1\), so \(Z=(52-50)/1=2\).
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 \(N\).
\[\dfrac{\bar X_n-\mu}{\sigma/\sqrt n}\ \xrightarrow{d}\ N(0,1)\]
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