Is there a routine available to derive the variable (i.e for any given z) for the standard normal loss function, L(z)?

If we know the value of L(z), how can z be determined?

I'm wondering if there is an available command that can evaluate the number of terms required to produce a desired outcome.

Specifically, I am interested in determining the probability of a Poisson distribution, given the parameter (mean) value and the probability outcome. I can obtain the desired result using trial and error / brute force, but I am curious to know if there is a more efficient way. 

Suppose that, lambda = 2.6 and the cumulative sum of the probabilities is 95%. I know that I must add the first 6 terms for P(x) in the series (x=0,1, ..,5) to sum to 0.95. Each term ...  P(x=0)= 0.07, P(x=1)=0.19, and so on.

However, how can we know that desired 95% outcome can be determined from the first 5 terms without trial & error?

Is there a simple command to generate decimal numbers in a given range? 

For example, I wish to obtain a randomly generated number between, say ... -0.5 and 0.5.

Given a basic list of data, is it possible to extract the distribution type /  equation / probability density function?

I was looking to see if anyone has come across a Maple routine for a savings algorithm - specifically, Clarke and Wright. In fact, any classical savings heuristic would also be interesting.

Any guidance would be truly appreciated.