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QUESTION
 Find approximately the probability that a Poisson variable with
  mean 20 takes the value 20.


ANSWER

$\phi(20)$ has $\mu=20,\ \sigma^2=20.\\
  P(X=20)=P(19.5&lt;Z&lt;20.5)\\
  P(Z&lt;20.5)=\Phi(\frac{20.5-20}{\sqrt{20}})=\Phi(0.112)=0.5444\\
  Hence P(19.5&lt;Z&lt;20.5)=0.5444-0.4556=0.0888\approx 0.09$
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