Exercise · ZW-NORMAL-DISTRIBUTION-002 · ★☆☆ Basic
If \(X\sim N(50,16)\), what is the standardized value \(z\) of \(x=58\)?
Choose one option.
Show answer
- B. \(2\)
Explanation
With \(\sigma=4\): \(z=(58-50)/4=2\). Dividing by the variance (16) instead of the standard deviation is a typical mistake.
Review the concept: Normal distribution
A normal variable is a continuous variable with density \(f\) shaped like a symmetric bell, determined by its mean \(\mu\) and its standard deviation \(\sigma\).
\[f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}\]
More practice problems: normal distribution
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