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**financial** I'm stuck but here's what I have so far. I'm trying to find the probability that S is bigger than T.

$\displaystyle T \sim N(18,4), S \sim N(20,1)$

$\displaystyle Pr \{S>T \} = Pr \{ \frac{S-20}{1} > \frac{T-20}{1} \}$

$\displaystyle =Pr\{N(0,1)>T-20\}$

$\displaystyle =Pr\{T-20<N(0,1)\}$

$\displaystyle \mbox{Let }X=T-20 \mbox{ then } X \sim N(18-20,4) \sim N(-2,4)$

$\displaystyle \Rightarrow Pr\{T-20<N(0,1)\}$

$\displaystyle =Pr\{X<N(0,1)\}$

$\displaystyle =Pr\{N(-2,4)<N(0,1)\}$

Where do I go from here?