36 Research on eating disorders. In The American Statistician

(May 2001) study of female students who suffer from bulimia, each student completed a questionnaire from which a

“fear of negative evaluation” (FNE) score was produced.

(The higher the score, the greater is the fear of negative evaluation.) Suppose the FNE scores of bulimic students have a distribution with mean m = 18 and standard deviation s = 5. Now, consider a random sample of 45 female students with bulimia.

a. What is the probability that the sample mean FNE score is greater than 17.5?

b. What is the probability that the sample mean FNE score is between 18 and 18.5?

c. What is the probability that the sample mean FNE score is less than 18.5?