if X is a normally distributed random variable and $ P( X \le x) = k $ find $ P( X \le 2\mu - x) $ in terms of k.
I tried standardizing the variable but don't know how 1-k is obtained as the solution.
Normal distribution question in terms of k
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probability
1 Answers
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$X$ is symmetric about $\mu$ i.e. $P(X\leq \mu-x)=P(X\geq \mu+x)$ for any $x\in\mathbb R$. $P(X\leq 2\mu-x)=P(X\leq \mu-(x-\mu))=P(X\geq \mu+(x-\mu))=P(X\geq x)=1-k$