An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 6982 fur seal pups were tagged in early August. In late August, a sample of 700 pups was observed, and 245 these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.
The estimated total number of fur seal pups in Rookery A is____.
Presumably, the same percentage of seals was tagged as was found in the later sample. So,
6982/x = 245/700
To estimate the total number of fur seal pups in Rookery A, we can use the proportion of tagged pups in the sample to the total tagged pups.
Step 1: Calculate the proportion of tagged pups in the sample:
Proportion of tagged pups = (Number of tagged pups in sample / Total number of pups in sample)
Proportion of tagged pups = (245 / 700)
Step 2: Calculate the total number of fur seal pups in Rookery A:
Total number of fur seal pups in Rookery A = (Proportion of tagged pups * Total number of pups in Rookery A)
Total number of fur seal pups in Rookery A = (245 / 700) * 6982
Simplifying the equation:
Total number of fur seal pups in Rookery A = (0.35) * 6982
Total number of fur seal pups in Rookery A = 2443.7
The estimated total number of fur seal pups in Rookery A is approximately 2443.
To estimate the total number of fur seal pups in Rookery A, we can use the concept of proportion. We know that 245 out of a sample of 700 pups were previously tagged.
To set up a proportion, we can use the formula:
(tagged pups in sample) / (total pups in sample) = (tagged pups in population) / (total pups in population)
Let's substitute the values we have:
245 / 700 = x / 6982
Cross multiplying, we get:
245 * 6982 = 700 * x
x = (245 * 6982) / 700
Calculating this, we find:
x ≈ 2440
Therefore, the estimated total number of fur seal pups in Rookery A is approximately 2440.