The composite ACT scores of entering freshmen at an area University have a N(24,4) distribution. Use this information to complete the following.
a) For one randomly selected entering freshman, what is the probability that their composite ACT score was greater than 30?
b) A random sample of 100 entering freshmen is selected. What is the distribution of the mean composite ACT score, for the University?
c. What is the probability that the mean composite ACT score for the 100 randomly chosen freshmen is less than 23?