Expand Your Knowledge: Geometric Distribution; Agriculture Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin (Source: Australian Journal of Agricultural Research, Vol. 25, pp. 783–790). (Bitter pit is a disease of apples resulting in a soggy core, which can be caused either by overwatering the apple tree or by a calcium defi ciency in the soil.) Let n be a random variable that represents the fi rst Jonathan apple chosen at random that has bitter pit.

(a) Write out a formula for the probability distribution of the random variable n.

(b) Find the probabilities that n 5 3, n 5 5, and n 5 12.

(c) Find the probability that n  5.

(d) What is the expected number of apples that must be examined to fi nd the fi rst one with bitter pit? Hint: Use m for the geometric distribution and round.

Hint: See Problem 23.