A lifeguard has to jump in to save a swimmer in trouble at the lake at Possum Park an average of 2 times a week, according to a Poisson distribution.
a. What is the probability that he will save more than 25 swimmers in the 10-week season he works?
b. If you know he saved exactly 1 swimmer on his 8-hour shift today, what is the chance he did it in the last hour that he worked?
c. If there are 5 lifeguards working independently, and they each have the same average rate for saving swimmers, what is the probability that exactly three of them will save more than 25 swimmers (each) in the 10-week season?
d. The lifeguards receive a small raise if they save 10 swimmers. How long will the lifeguard expect to wait for his raise?
e. What is the probability our lifeguard have to wait at least 1 week after the start of the summer until he saves his first swimmer?
f. How many independent lifeguards will we expect to have to ask until we find our second lifeguard who had to wait at least 1 week after the start of the summer until he/she saved his/her first swimmer?