Intelligence Quotients. Measured on the Stanford Revision of the Binet–Simon Intelligence Scale, intelligence quotients (IQs)

are known to be normally distributed with a mean of 100 and a standard deviation of 16. Use the technology of your choice to do the following.

a. Simulate 1000 samples of four IQs each.

b. Determine the sample standard deviation of each of the 1000 samples.

c. Obtain the following quantity for each of the 1000 samples:

n − 1

σ2 s2 = 4 − 1 162 s2

.

d. Obtain a histogram of the 1000 values found in part (c).

e. Theoretically, what is the distribution of the variable in part (c)?

f. Compare your answers from parts

(d) and (e).