An inspector inspects a shipment of medications to determine the efficacy in terms of the proportion p in the shipment that failed to retain full potency after 60 days of production. unless there is clear evidence that this proportion is less than 0.05, she will reject the shipment. to reach a decision, she will test the following hypotheses using the large-sample test for a population proportion:
h0 : p = 0.05, ha : p < 0.05
to do so, she selects an srs of 200 pills. suppose that eight of the pills have failed to retain their full potency.
the p-value of the test is?

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)