A local college reported that the average SAT score of its students is 1100 with a standard deviation of 45. Dr. Smith drew a random sample of 100 students from this college and found that her sample mean was 1091. a. What is the z statistic for this sample? Show your work. b. Is Dr. Smith's sample representative of the students at this college? Explain your reasoning.

4. According to the 2012-2013 annual report of the American Psychological Association's survey of faculty salaries in graduate departments of psychology, the average salary for a new (less than 3 years) professor was $92,000, with a standard deviation of $32,845. Assuming that these data are normally distributed: a. What was the salary for a new full professor in the 98th percentile? b. What percentage of new professors earn less than $60,000?