Cats live for 14 years, on average, with a standard deviation of 2 years. A simple random sample of 78 recently deceased cats is selected, and the sample mean age at death x̄ of these cats 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 for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately Normal, regardless of the distribution of the population. Since the sample size is 78, the sample mean age at death x̄ will have an approximately Normal distribution.

Cats Live for 14 Years, on Average, with a Standard