Pyramid Lake is located in Nevada on the Paiute Indian Reservation. This lake is famous for large cutthroat trout. The mean number of trout (large and small) caught from a boat is 0.667 ­fish per hour (Reference: Creel Chronicle, Vol. 3, No. 2).

Suppose you rent a boat and go fi­shing for 8 hours. Let r be a random variable that represents the number of fi­sh you catch in the 8-hour period.

(a) Explain why a Poisson probability distribution is appropriate for r. What is l for the 8-hour fi­shing trip? Round l to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities.

(b) If you have already caught three trout, what is the probability you will catch a total of seven or more trout? Compute P(r ³ 7 | r ³ 3).

(c) If you have already caught four trout, what is the probability you will catch a total of fewer than nine trout? Compute P(r ³ 9 | r ³ 4).

(d) List at least three other areas besides ­fishing to which you think conditional Poisson probabilities can be applied.