Researchers who study the abundance of the flour beetle, Tribolium castaneum, have developed a probability density function that can be used to estimate the abundance of the beetle in a population. The density function, which is a member of the gamma distribution, is ƒ(x) = 1.185 * 10^-9x^4.5222e^-0.049846x, where x is the size of the population.

(a) Estimate the probability that a randomly selected flour beetle population is between 0 and 150.
(b) Estimate the probability that a randomly selected flour beetle population is between 100 and 200.