$S$ and $W$ are independent random variables with the distributions $\mathrm{N}\left( 20,25 \right)$

Question

$S$ and $W$ are independent random variables with the distributions $\mathrm{N}\left( 20,25 \right)$ and $\mathrm{N}\left( \mu ,{{\sigma }^{2}} \right)$ respectively. It is known that $\mathrm{P}\left( W\le 10 \right)=\mathrm{P}\left( W>13 \right)$ and $\mathrm{P}\left( S>2W \right)=0.43$. Calculate the values of $\mu $ and $\sigma $ correct to three significant figures. [4]

Accepted Answer

$\mu =\frac{23}{2}$ and $\sigma =8.13$ ($3$ s.f.)

Determining Parameters of a Normal Distribution from Probability Conditions

Determining Parameters of a Normal Distribution from Probability Conditions

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