A wildlife biologist estimates total weight of fish in a lake using ratio estimation. A sample of 100 fish yields: mean weight ȳ = 2.5 kg, mean scale surface area x̄ = 0.45 m² (easy to measure from photos). From aerial surveys, the population mean scale area is known: X̄ = 0.48 m². The lake contains N = 50,000 fish. Using ratio estimation:

$\hat{Y}_{ratio} = \frac{\bar{y}}{\bar{x}} \times \bar{X} \times N$

What is the estimated total weight?