The average age of trees in a large local park is 60 years, with a standard deviation of 2.2 years. A simple random sample of 400 trees is selected, and the sample mean age x̄ of these trees is computed. What is the probability that the average age x̄ of the 400 trees is more than 60.1 years?

Question

Quizplus · Accepted Answer

We need to use the central limit theorem, which tells us that the sample mean follows a normal distribution with mean μ = 60 and standard deviation σ/√n = 2.2/√400 = 0.11. Thus, we have:

Z = (x̄ - μ) / (σ/√n) = (60.1 - 60) / 0.11 = 0.9091

Using a standard normal distribution table or calculator, we find that the probability of Z being greater than 0.9091 is approximately 0.1814. Therefore, the answer is B.

The Average Age of Trees in a Large Local Park