The mean of a population is 74 and the standard deviation is 13. The shape of the population is unknown. Determine the probability of each of the following occurring from this population.
Appendix A Statistical Table
a. A random sample of size 32 yielding a sample mean of 77 or more
b. A random sample of size 150 yielding a sample mean of between 72 and 77
c. A random sample of size 221 yielding a sample mean of less than 74.5
(Round all the values of z to 2 decimal places and final answers to 4 decimal places.)