Normal Approximation to Poisson Distribution
Normal distribution can be used to approximate the Poisson distribution when the mean of Poisson random variable is sufficiently large.
Let $X$ be a Poisson distributed random variable with mean $\lambda$.
The mean of $X$ is $\mu=E(X) = \lambda$ and variance of $X$ is $\sigma^2=V(X)=\lambda$.
The general rule of thumb to use normal approximation to Poisson distribution is that $\lambda$ is sufficiently large (i.e., $\lambda \geq 5$).
For sufficiently large $\lambda$, $X\sim N(\mu, \sigma^2)$. That is $Z=\frac{X\mu}{\sigma}=\frac{X\lambda}{\sqrt{\lambda}} \sim N(0,1)$.
Normal Approx. to Poisson Distribution  

Parameter ($\lambda$)  
Select an Option  
Enter the value(s) : 


Results  
Mean ($\mu=\lambda$)  
Standard deviation ($\sqrt{\lambda}$)  
Required Probability : 
Formula
 $P(X=A)=P(A0.5<X<A+0.5)$
 $P(X<A)=P(X<A0.5)$
 $P(X\leq A)=P(X<A+0.5)$
 $P(A< X\leq B)=P(A0.5<X<B+0.5)$
 $P(A\leq X< B)=P(A0.5<X<B0.5)$
 $P(A\leq X\leq B)=P(A0.5<X<B+0.5)$