A hybrid-grower is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: many of the ears contained no borers. Some ears had one borer; a few had two borers; and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The grower counted 3,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?
A) 0.3476
B) 0.4966
C) 1.000
D) 0.0631

Question

Quizplus · Accepted Answer

The average number of borers per ear is calculated by dividing the total number of borers by the total number of ears, which is 3,500 borers / 5,000 ears = 0.7 borers per ear. Using the Poisson distribution formula for the probability of getting exactly k events (k = 0 borers in this case) when the average rate of occurrence is λ (0.7 borers per ear), the formula is P(k; λ) = (e^(-λ) * λ^k) / k!. For k = 0, this simplifies to P(0; 0.7) = e^(-0.7) * 0.7^0 / 0! = e^(-0.7). Calculating e^(-0.7) gives approximately 0.4966, which means there is about a 49.66% chance an ear of corn selected at random will contain no borers.

A Hybrid-Grower Is Experiencing Trouble with Corn Borers