Confidence Interval for Poisson Distribution

#1
Hi ,

I am trying to calculate a 90% Confidence Interval for a Poisson Distribution.

The Question is as below. Please let me know how is the first equation and second equation formed.

Confidence Interval.png
 

Dason

Ambassador to the humans
#2
If you knew what lambda was would you be able to calculate probabilities for the poisson distribution?