Using the telephone numbers listed below as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits.
4142862500
4148988818
4142568453
4143733087
4142073585
4148918490
4142286901
4148988500
4148468334
4142955229
4147354784
4143225186
4144085526
4143745000
4148344169
4142299314
4147411100
4147864274
4146041290
4148916660
a. Calculate the mean of the 20 samples
b. Draw a 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. Describe 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 the 20 new x-bars to the histogram in part b. Describe 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!