Consider the undergraduate student population at syracuse. Suppose the true mean GPA in that population (mu) is 3.2, while the true standard deviation (sigma) is 0.2. In addition, the distribution of GPA is not normal (it is not symmetric and bounded between 0 and 4) in this population.

a. If you pick a random sample of 30 students, what is the probability to observe a sample average below 3.15?

b. If you pick a random sample of 30 students, what is the probability to observe a sample average between 3.15 and 3.25?

c. If you pick a random sample of 60 students, what is the probability to observe a sample average between 3.15 and 3.25?

d. Why is it preferable to sample 60 students rather than 30?