Given that $X$~$N\left( 1.6,\ 4 \right)$, find $\mathrm{P}\left( \left| X-1.6 \right|0.4 \right)$.

Question

Given that $X$~$N\left( 1.6,\ 4 \right)$, find $\mathrm{P}\left( \left| X-1.6 \right|>0.4 \right)$. Find the set of values of ${a}$ if $\mathrm{P}\left( X>a \right)\ge 0.99$, where $X$~ $N\left( 20,\ 25 \right)$. The random variable ${Y}$ has a normal distribution with mean ${10}$ and standard deviation ${2}$. Find the value of the constant ${k}$ such that $\mathrm{P}\left( 10-k

Accepted Answer

(a) $0.841$; (b) $a \leq 8.37$; (c) $k = 3.92$

ACJC Normal Distribution Tutorial Q6

ACJC Normal Distribution Tutorial Q6

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