The number of (large) inclusions in cast iron follows a Poisson distribution with a mean of 2.5 per cubic millimeter. Approximate the following probabilities:

(a) Determine the mean and standard deviation of the number of inclusions in a cubic centimeter (cc).

(b) Approximate the probability that fewer than 2600 inclusions occur in a cc.

(c) Approximate the probability that more than 2400 inclusions occur in a cc.

(d) Determine the mean number of inclusions per cubic millimeter such that the probability is approximately 0.9 that 500 or fewer inclusions occur in a cc.