A new cure has been developed for a certain type of cement that results in a compressive strength of 5000 kilograms per square centimeter and a standard deviation of 120. To test the hypothesis that p = 5000 against the alternative that p < 5000, a random sampling-apple of 50 pieces of cement is tested. The critical region is defined to be  < 4970.
(a) Find the probability of committing a type \ error when Hn is true
(b) Evaluate 0 for the alternatives p = 4970 and p = 1960.