Risk pooling and life insurance.

When you pool risk then the probability for everyone in that pool to incur higher losses decreases. Also when you have about 20 or more people in the pool, the distribution of the losses becomes normal. So the more people you add the closer you get to a true normal distribution. Also, as you add more people the mean might increase a little but the standard deviation will decrease. This will create a slimmer normal distribution (with different size and scale parameters), that have most of the losses occurring around the mean, and a smaller probability of being in the tail.

From the central limit theorem:

E(Xi) = n*E(X)
Var(Xi)= n*Var(X)

You then use the new variance and the expected value from a given distribution to standardize the distribution into a normal distribution. Then you can use the Z score table to find percentiles that you are interested in.

Z=(X-E(X))/standard deviation