P(X =< 31)
Z = X - μ/σ
= 31-30/30^1/2
= 0.183
-> Φ(0.183)
= 0.5726
The Answer is 0.608
2026-04-04 03:54:11.1775274851
Using the Normal Approximation to the Poisson Distribution, where appropiate, If X ~ Po(30) find P(X=<31)
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Note that $\Pr(X\le31) = \Pr(X<32).$ So do you use $\dfrac{31-30}{\sqrt{30}}$ or $\dfrac{32-30}{\sqrt{30}}\text{?}$
They are both approximations. In this situation just using the number halfway between those -- that is called a "continuity correction": $$ \Phi\left( \frac{ 31.5 - 30}{\sqrt{30}} \right) \approx 0.6079. $$