Given that $X$~$N\left( \mu ,\ 2.5 \right)$, and $\mathrm{P}\left( X3.5 \right)=0.970$, find $\mu $

Question

Given that $X$~$N\left( \mu ,\ 2.5 \right)$, and $\mathrm{P}\left( X>3.5 \right)=0.970$, find $\mu $. Two independent observations of $X$ are denoted by ${{X}_{1}}$ and ${{X}_{2}}$. Find $\mathrm{P}\left( \left| {{X}_{1}}-{{X}_{2}} \right| The random variable $S$ is the sum of $n$ independent observations of $X$. State the approximate value of $\mathrm{P}\left( S>3.5n \right)$ as $n$ becomes very large, justifying your answer.

Accepted Answer

$6.47$ (a) $0.975$ (b) $1$

ACJC Normal Distribution Tutorial Q7

ACJC Normal Distribution Tutorial Q7

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