Question

Let's say there's a farm full of apple trees that have been infested and damaged by pests. If 0.35 is the probability that an apple tree from the farm has no more than 5 damaged apples, and a random sample of 20 apple trees is taken from the farm, what does (0.35)^20 represent in the context of this problem? How would you formally phrase the response to this on an exam?

(AP Statistics question)

Answer 1

Probability that a tree has no more than 5 damages apples is 0.35. We have a sample of 20 trees. Thus, probability that none of these 20 trees have more than 5 damaged apples is 0.35^(20) [since probabilities of independent events get multiplied]. Thus 0.35^20 represents the probability that none of the apple trees have more than 5 damages apples.

The following can be a formal formulation: