Question

Emperor penguins defend an area around their nests. Their territory encompasses a complete circle around the nest with approximately a 0.5 m radius. If each nesting penguin has this same size and shape territory, what type of distribution will these animals exhibit?

Answer 1

The distribution that the animals will exhibit shall be uniform circular distribution.

Explanation:

The uniform circular distribution in a circular disc of radius 'R' is given by

`f(x)=\frac{2\sqrt{R^(2)-x^(2)}}{\pi R^(2) }(-R< x< +R)\\\\f(x)=0(x> +R,x< -R)`

Applying values we get

`f(x)=\frac{2\sqrt{0.5^(2)-x^(2)}}{\pi 0.5^(2) }(-R< x< +R)\\\\f(x)=2.54\sqrt{0.5^(2)-x^(2)}`