Question

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 of these cats is computed. We know that the random variable has an approximately Normal distribution because of

a. the law of large numbers.

b. the fact that probability is the long-run proportion of times an event occurs.

c. the 68–95–99.7 rule.

d. the central limit theorem

Answer 1

Central limit theorem tells us:

If the simple random sample of size n is selected from a distribution with mean and standard deviation , then the distribution of sample means approaches a normal distribution.

The greater the sample size, the better the approximation.

n > 30

In our example n = 78 > 30

The correct option is

d. the central limit theorem