Agriculture: Apples Approximately 3.6% of all (untreated)

Chapter , Problem 8

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Agriculture: Apples 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. 783790). (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 deficiency in the soil.) Let n be a random variable that represents the first 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 3, n 5, and n 12. (c) Find the probability that n 5. (d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use m for the geometric distribution and round.

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