Using the phone numbers listed in your telephone directory as your population, randomly obtain 20 samples of size $3 .$ From each phone number identified as a source, take the fourth, fifth, and sixth digits. (For example, for $245-8268,$ you would take the $8,$ the $2,$ and the 6 as your sample of size $3 .$ )
a. Calculate the mean of the 20 samples.
b. Draw a histogram showing the 20 sample means. (Use classes $-0.5 \text { to } 0.5,0.5 \text { to } 1.5,1.5 \text { to } 2.5, \text { and so on. })$
c. Describe the distribution of $\bar{x}$ 's that you see in part $b$ (shape of distribution, center, and amount of dispersion).
d. Draw 20 more samples and add the 20 new $\bar{x}$ 's to the histogram in part b. Describe the distribution that seems to be developing.