Approximately 7.8% of all (untreated) Jonathan apples had

Last updated: 7/9/2022

Approximately 7.8% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin. (Bitter pit is a disease of apples resulting in a soggy ore, 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. (Use p and n in your answer.) P(n)= (b) Find the probabilities that n = 3, n = 5, and n 12. (Use 3 decimal places.) P(3) P(5) P(12) (c) Find the probability that n 2 5. (Use 3 decimal places.) (d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use for the geometric distribution and round.