Boys of a certain age are known to have a mean weight of μ = 85 pounds. A complaint is made that the boys living in a municipal children's home are underfed. As one bit of evidence, n = 36 boys (of the same age) are weighed and found to have a mean weight of 80.11 pounds. It is known that the population is normally distributed with standard deviation σ = 10.6 pounds. Based on the available data, what should be concluded concerning the complaint?

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)