Exercise · ZW-NORMAL-DISTRIBUTION-010 · ★★★ Advanced
Let \(X\sim N(2,\sigma^2)\) with \(P(X>5)=0.1\). What is \(P(X<-1)\)?
Choose one option.
Show answer
- A. \(0.1\)
Explanation
The points \(5\) and \(-1\) are at the same distance from \(\mu=2\) (at \(\pm3\)). By symmetry the tails are equal: \(0.1\).
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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