Question

1) You are studying staghorn sculpin within wetland creeks, and you use baited minnow traps separated by 10 meters. After an hour, you pull all your minnow traps up and count the number of sculpins found in each minnow trap. You organize the data in a frequency table seen below:

Number Sculpins	Obs. Freq.
0	13
1	15
2	24
3	8
4	31
5	16
6	29
7	9
>7	0

a) Calculate and record the CD
b) What does your calculated CD tell you about the staghorn sculpin distribution?
c) If you were to repeat this experiment, how many minnow traps would you expect to find 5 staghorn sculpins?
d) If you were to repeat this experiment, what is the probability you would find a minnow trap with at least one sculpin?

Answer 1

The data is about the number of sculpins that are being recorded from minnow traps. The data is:

Number Sculpins	Obs. Freq.
0	13
1	15
2	24
3	8
4	31
5	16
6	29
7	9
>7	0

a) We are to calculate cumulative distribution or CD. To do this, we calculate the sum of frequencies of all the categories prior to the current category. Doing so, we get:

Number Sculpins	Obs. Freq.	CD
0	13	13
1	15	28
2	24	52
3	8	60
4	31	91
5	16	107
6	29	136
7	9	145
>7	0	145

b) Plotting the CD, we see:

As can be seen, the CD appears to increase more or less linearly up to 6 sculpins, after which it plateaus off. Therefore, the frequency is more or less similar for sculpin count up to 6.

c) The repeat experiment should be reliable with the current experiment whose data is available. And hence the relative number of minnow traps in which we get 5 sculpins should stay the same. This relative number is 16/145 = 0.1103 = 11%. Hence approximately, 11% of the minnow traps in the repeat experiment should have 5 sculpins.

d) Let X be the random variable that determines the number of sculpins found. Hence, we are to determine here: