The University Dean has asked you to perform this study on all students studying business within Australia. It is known that the population is normally distributed with a mean is 67 and a standard deviation of 21. To conduct this study, a random sample of 100 students is selected.
(a) Calculate the appropriate standard error required.
(b) Calculate the respective z-score you would use to determine the probability that the sample mean grade will be less than 75.
(c) Determine the probability that the sample mean grade will be less than 75.
Please give me complete answer with all steps in detail.