A marine biologist tags 100 whales. Later, a sample of 115 whales was gathered and 5 were tagged. Estimate the total whale population.

This is a hypergeometric distribution problem.

Assuming that the tagged whales are subsequently randomly distributed in the whale population, we have population N, where
N = (115/5)*100 = 2300 approximately.

For more accurate estimations, use the hypergeomatric distribution and maximize P(5).

To estimate the total whale population, we can use the concept of "mark and recapture." This method assumes that the proportion of tagged whales in the sample reflects the proportion of tagged whales in the entire population.

Let's break down the information we have:

- The biologist initially tagged 100 whales.
- Later, a sample of 115 whales was gathered.
- In this sample, 5 of the whales were tagged.

Now, we can use a proportion to estimate the total population:

Number of tagged whales in initial population / Total population = Number of tagged whales in the sample / Sample size

Let's plug in the values we have:

100 / Total population = 5 / 115

To solve for the total population, we can cross-multiply and then solve for Total population:

5 × Total population = 100 × 115
Total population = (100 × 115) / 5

Total population ≈ 2,300

Based on this calculation, the estimated total whale population is around 2,300 whales.