A certain scientific theory supposes that mistakes in cell division occur according to a Poisson process with rate 2.5 per year, and that an individual dies when 196 such mistakes have occurred. Assuming this theory, find

(a) the mean lifetime of an individual,

(b) the variance of the lifetime of an individual.

Also approximate

(c) the probability that an individual dies before age 67.2,

(d) the probability that an individual reaches age 90,

(e) the probability that an individual reaches age 100.