EXAMPLE 5.10

Using the Central Limit Theorem applet. In Example 5.9, we considered sample sizes of n = 2, 10, and 25 from an exponential distribution. Figure 5.9 shows a screenshot of the Central Limit Theorem applet for the exponential distribution when n = 10. The mean and standard deviation of this sampling distribution are 1 and , respectively. From the 10,000 SRSs, the mean is estimated to be 1.001 and the estimated standard deviation is 0.319. These are both quite close to the true values. In Figure 5.8(c), we saw that the density curve for 10 observations is still somewhat skewed to the right. We can see this same behavior in Figure 5.9 when we compare the histogram with the Normal curve based on the central limit theorem.