Approximating discrete distribution by continuous distribution

On Tue, Jan 22, 2013 at 11:49 AM, Michael Haenlein

I would like to find a continuous approximation of this discrete
distribution in order to estimate the probability that a person is for
example 16 years old.

Given that people age continuously (and continually...), you sound
like you are trying to replace one discrete distribution with another
(discretised by year).

 A continuous distribution would give you, for example, the
probability that a person is between 16.0 and 16.1 years old.

Barry