On a police sergeant's examination, the historical mean score was 80 with a standard deviation of 20. Four officers who were alleged to be cronies of the police chief scored 195, 171, 191, and 189, respectively, on the test. This led to allegations of irregularity in the exam.
(a) Convert these four officers' scores to standardized z-values.
(b) Do you think there was sufficient reason to question these four exam scores? What assumptions are you making? (Data are from Detroit Free Press, March 19, 1999, p. 10A.)