5.65 Change the sample size to 12.

Refer to Exercise 5.63. Change the sample size to 12 and answer parts (a) through (c) of that exercise. Note that the theoretical mean of the sampling distribution is still 0.5 but the standard deviation is the square root of 1/144 or, simply, 1/12. Investigate how close your simulation estimates are to these theoretical values. In general, explain the effect of increasing the sample size from two to 12 using the results from Exercise 5.63 and what you have found in this exercise.