An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane. If 2 swimmers are in a lane, each swims up and down one side of the lane. Swimmers always join the lane with the fewest number of swimmers. If all 3 lanes are occupied by 2 swimmers, a prospective swimmer becomes disgusted and goes running.

a. What fraction of the time will 3 people be swimming laps?

b. On the average, how many people are swimming laps in the pool?

c. How many lanes does the YMCS need to allot to lap swimming to ensure that at most 5% of all prospective swimmers will become disgusted and go running?