Inclusions are defects in poured metal caused by contaminants. The number of (large) inclusions in cast iron follows a Poisson distribution with a mean of 2.5 per cubic millimeter. Determine the following:

(a) Probability of at least one inclusion in a cubic millimeter.

(b) Probability of at least five inclusions in 5.0 cubic millimeters.

(c) Volume of material to inspect such that the probability of at least one inclusion is 0.99.

(d) Instead of a mean of 2.5 per cubic millimeters, the mean inclusions per cubic millimeter such that the probability of at least one inclusion is 0.95.