The number of claims per year from a particular auto insurance policy has a Poisson distribution with a mean of 1, and probability function pk. Based on a number of years of experience, the insurer decides to change the distribution, so that the new probability of 0 claims is p0* = .5, and the new probabilities pk* for k > = 1 are proportional to the old (Poisson) probabilities according to the relationship pk* = c . pk for k > = 1. Find the mean of the new claim number distribution.

A) .79
B) .63
C) .5
D) .37
E) .21