A consulting organization predicts whether corporations' earnings for the coming year will be unusually low, unusually high, or normal. Before deciding whether to continue purchasing these forecasts, a stockbroker compares past predictions with actual outcomes. The accompanying table shows proportions in the nine joint classifications. OUTCOME PREDICTION UNUSUALLY HIGH NORMAL UNUSUALLY LOW Unusually high Normal 23 06 Unusually low .01 228 12 .03 .08 .19

(a) What proportion of predictions have been for unusually high earnings?

(b) What proportion of outcomes were for unusually high earnings?

(c) If a firm were to have unusually high earnings, what is the probability that the consult- ing organization would correctly predict this event?

(d) If the organization predicted unusually high earnings for a corporation, what is the probability that these would materialize?

(e) What is the probability that a corporation for which unusually high earnings had been predicted will have unusually low carnings?