Question

Power companies trim trees growing near their lines to avoid power failures due to falling limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees. The power company tests this chemical on 250 sycamores. Consider these as an SRS from the population of all sycamore trees. What is the probability that at least 60 trees (24% of the sample) are killed?

Answer 1

To find the probability that at least 60 trees are killed, we can use the binomial probability formula. X follows a binomial distribution with n = 250 and p = 0.2. Calculate P(X < 60) and subtract it from 1 to find the probability of at least 60 trees being killed.

Step-by-step explanation:

To find the probability that at least 60 trees are killed, we can use the binomial probability formula:

P(X >= k) = 1 - P(X < k)

Where X is the number of trees killed, k is the desired number of trees killed, and P(X < k) is the cumulative probability of X being less than k. In this case, X follows a binomial distribution with n = 250 (the number of sycamores tested) and p = 0.2 (the probability of killing a tree).

We can calculate P(X < 60) using a binomial calculator or a statistical software, and then subtract it from 1 to find the probability of at least 60 trees being killed.