Question
A random variable $X \sim N(0,1)$. Find $P(X>0)$ and $P(X<0)$
✓
Answer
Given X ∼ N(0, 1)
∴ μ = 0
$\therefore P(X>\mu)=P(X>0)=\frac{1}{2}$ as the distribution is symmetric about $\mu=0$.
$P(X<\mu)=P(X<0)=\frac{1}{2}$ as the distribution is symmetric about $\mu=0$.
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