You need to show your work (formula setup, calculations, etc.) and state any properties or rules you need to solve the problem.

1) Suppose that we are interested in the mean number of points scored by a basketball team in a given game for a population of professional basketball teams. We take a random sample of size n = 35. Then suppose we know from past data the mean number of points scored is 101 and the standard deviation is 5.

a) Do we know the distribution of the parent population? If so, what is it?

b) What is the distribution of the sample mean?

c) What is the probability of observing a team score less than 80 points in a game?

d) What is the probability of observing a sample mean less than 98 points per game if we added an additional 25 games to our sample?