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