A farmer who grows genetically engineered corn 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 farmer 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. The probability of an ear having no borers in a Poisson distribution is given by $P(X=0) = e^{-\lambda}$, where $\lambda$ is the average rate (0.7 in this case). Therefore, $P(X=0) = e^{-0.7} \approx 0.4966$.

A Farmer Who Grows Genetically Engineered Corn Is Experiencing Trouble