Question: The grade point averages (GPAs) of all students enrolled at a large university have a normal distribution with a population mean of 3.02 and a population standard deviation of 0.29. A random sample of 16 students is drawn from the Registrar’s list. For part (a), be sure to use the z-calculation that is for sample means. I am presenting it to steer you in the right direction:

Z = \[(\bar{x}\] - m)/(s/ \[\sqrt{n}\] ).

It is important that you understand this expression. See the text starting on page 261.

a. What is the probability that the sample mean GPA calculated from your random sample of 16 students is 3.10 or higher?

b. What is the probability that the GPA of an individual randomly selected from the Registrar’s list is 3.10 or higher?

c. Why do I need to state that the distribution of GPAs for individual students is normal in order to do part (c) of this problem? Please answer in a single sentence.