You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean in the world. Crab populations and commercial catch rates are highly variable, but the fishery is under constant pressure from overfishing, habitat destruction, and pollution. These days, you tend to pull crab pots containing an average of 2.4 crabs per pot. Given that you are economically challenged as most commercial fishermen are, and have an expensive boat to pay off, you’re always interested in projecting your income for the day. At the end of one day, you calculate that you’ll need 7 legal-sized crabs in your last pot in order to break even for the day. Use these data to address the following questions. Show your work.
a. What is the probability that your last pot will have the necessary 7 crabs? (5 points)
b. What is the probability that your last pot will be empty? (5 points)
| this is Poisson distribution with parameter λ=2.4 |
a)
probability that your last pot will have the necessary 7 crabs:
| P(X=7)= | {e-2.4*2.47/7!}= | 0.0083 |
b)
probability that your last pot will be empty :
| P(X=0)= | {e-2.4*2.40/0!}= | 0.0907 |
You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus),...