## Math Forum - Problem of the Week

### Fish Farm II

Please keep in mind that this is a research project, and there may sometimes be glitches with the interactive software. Please let us know of any problems you encounter, and include the computer operating system, the browser and version you're using, and what kind of connection you have (dial-up modem, T1, cable).

Fish Farm II

### A Carp Family Picnic

The day after their birthday, the Carp triplets visit Lake Mark Park. Seeing some fish swimming in the lake, Angel scoops one out with a small net, then throws it back. It's a male . Angel then scoops out and throws back another fish, this time a female .

Excitedly, Angel says, "I think this lake has equal numbers of male and female fish, just like my pond at home!" (See Fish Farm I.)

Molly and Gar wonder whether the ratio of fish in the lake might be closer to the ratios in their own backyard ponds. (Recall that Molly's pond contains three times as many males as females, and Gar's pond has twice as many females as males. The triplets think they will need to do more "scooping" before reaching a conclusion about the lake's male-to-female fish ratio.

To Do: Use the applet to simulate scooping out fish from the lake. With a small net, you can only scoop out and throw back one fish at a time; however, in the applet, you can change the number of scoops you do in a row. Try changing the number of scoops to 10, 20, 50, or any other number of scoops you feel are needed to get a good estimate of the ratio of male to female fish. Be sure to save all your data to the table to use in answering the questions below.

### Questions

1. Which triplet's back-yard pond most closely matches the male:female ratio in the lake? Justify your answer with data you collect. In your explanation, tell us which display(s) of data you used to help you and how it helped. Remember, Angel's pond has a 1:1 ratio, Molly's pond has a 3:1 ratio [three times as many males as females], and Gar's pond has a 1:2 ratio [twice as many females as males].

2. What is your best estimate of the percentage of male fish in Lake Mark? Describe the strategy you used to determine this estimate.

3. How confident are you that your estimate is close to the actual percentage of male fish? What makes you feel confident about your estimate, and what would make you feel more confident?

Bonus: Suppose we knew that Lake Mark had just been filled with 350 male and 650 female fish. About how many male and female fish might be caught if you scooped a fish 10 times? What if you scooped a fish 700 times? How confident are you that your prediction would be close to an actual sample? Explain your reasoning.

 © 1994-2005 The Math Forum http://mathforum.org/pow/