hello, Can someone help me answer this with working out.

A private school promoted itself by advertising that its graduates had an average SAT verbal score of 550 (with a standard deviation of 100). At the end of the school year the Parent-Teacher Association (PTA) decided to test this contention and obtained the SAT verbal scores for 80 graduating seniors. Their average score was 532. What should the PTA conclude in regard to the school's claim if a .05 level of significance is used?

(a) Clearly state null and research hypotheses.

(b) What is the comparison distribution?

(c) What are the standard normal cut-off values for a test with significance level of 0.05?

(d) What is the observed Z score?

(e) Test your hypotheses and state your conclusions.