There is something that puzzles me. I tried calculating a Poisson probability. Exactly, and with the normal distribution, using both the continuity and without the continuity correction. However the answer became much more exact if I did it not using continuity correction, do you see why?

It is a poisson distribution with parameter \(\lambda=168\).

I want to calculate \(P(X \ge 196)\).

I get that the exact answer is:

0.01876504

The answer using CLT and continuity correction :0.01693269

And without the continuity correction I get: 0.01862127

R-code:

Code:

```
1-ppois(195,168) #exact
1-pnorm((195.5-168)/sqrt(168)) #with correction
1-pnorm((195-168)/sqrt(168)) #without correction
```