Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as the source, take the fourth, fifth, and sixth digits.
a. Compute the mean of the 20 samples
b. Draw histogram showing the 20 sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, 1.5 to 2.5 and so on).
c. Explain the distribution of the x-bars that you see in part b (shape of distribution, center, and the amount of dispersion).
d. Draw 20 more samples and add 20 new x-bars to histogram in part b. Explain the distribution that seems to be developing.
Use the empirical rule to test for normality. See the sampling distribution of sample means and the central limit theorem develop from your own data!