Psychomotor retardation scores for a particular group of manic-depressive patients have approximately a normal distribution with a mean of 930 and a standard deviation of 130. A random sample of 20 patients from the group was selected, and their mean psychomotor retardation score was obtained.
a. What is the probability that their mean score was between 900 and 960?
b. What is the probability that their mean score was greater than 960?
c. What is the 90th percentile of their mean scores?