Final answer:
To estimate the total number of trout in the lake using the mark and recapture method, you can set up a proportion and solve for the total population size. Based on the given information, the estimated total population size is approximately 760 trout.
Step-by-step explanation:
In order to estimate the total number of trout in the lake, we can use the mark and recapture method. We initially catch a sample of trout and tag them, then release them. The next day, we catch another sample and count how many of them were tagged. We can then use this information to estimate the total population size.
Based on the information given, the initial sample consisted of 95 tagged trout. The second sample consisted of 64 trout, of which 8 were tagged. To estimate the total population size, we can set up a proportion:
(Number of tagged trout in the initial sample) / (Total population size) = (Number of tagged trout in the second sample) / (Size of the second sample)
Plugging in the values:
(95) / (Total population size) = (8) / (64)
Cross multiplying:
8(Total population size) = 95 * 64
Simplifying:
Total population size = (95 * 64) / 8
Total population size ~ 760