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. We know the random variable x̄ has an approximately Normal distribution, but why?

Question

Quizplus · Accepted Answer

The central limit theorem states that the sample mean of sufficiently large sample sizes from any population with a finite mean and variance will be approximately normally distributed. In this case, we have a sample size of 400 which satisfies the requirement for "sufficiently large" according to the central limit theorem. Therefore, x̄ has an approximately Normal distribution.

The Average Age of Trees in a Large Local Park