Dr. ilvento uses a smart phone app to track the distance he walks. while taking the same walk each time, he noticed the distance stated in the app varied a lot. so he began to record the distance in an experiment. he also recorded the distance in a car and found it to be consistently 2.4 miles. the data and some summary information are given below. assume this comes from a normal distribution. this is a small sample mean problem.

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)