Business Statistics

Chapter 8 | Sampling and Sampling Distributions 271

8.10 CENTRAL LIMIT THEOREM

According to the central limit theorem, if a population is normally distributed, the sample means for

samples taken from that normal population are also normally distributed regardless of sample size. A

population has a mean  and standard deviation . If a sample of size n is drawn from the population

for sufciently large sample size (n  30); the sample means are approximately normally distributed

regardless of the shape of the population distribution.

Mathematically, it can be shown that the mean of the sample means is the population mean, that is,

 =

x

