Exercise · ZW-NORMAL-DISTRIBUTION-009 · ★★★ Advanced
If \(X\sim N(\mu,\sigma^2)\), approximately what is \(P(X\le\mu+\sigma)\)?
Choose one option.
Show answer
- B. \(0.84\)
Explanation
Standardizing, \(P(Z\le1)\approx0.8413\). The 0.68 is the probability of \(\mu\pm\sigma\); here the whole left half is also included: \(0.5+0.34\).
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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- ZW-NORMAL-DISTRIBUTION-008 If Z is standard normal, what is E[Z^2]?