Additives such as trace minerals, antibiotics, vermifuges, and insecticides are incorporated into animal feeds in parts per million (ppm). For effective mixing, the additives may be compressed into pellets the size of the ground grain in the feed and then colored with vegetable dye for easy identification. Quality control for thoroughness of mixing can be maintained by scooping out a known volume of the mixed feed and counting the number of colored pellets of additives. If properly mixed feed yields a Poisson process with l ¼ 2.5 per scoop, find:
a. The probability that a scoop will contain no pellets of additive
b. The probability that a scoop will contain exactly 1 such pellet
c. The probability that a scoop will contain at least 1 pellet
d. The outcomes that are most likely to occur approximately 80% of the time