The rare booted eagle of western Europe was the focus of a study by S. Suarez et al. to identify optimal nesting habitat for this raptor. According to their paper “Nesting Habitat Selection by Booted Eagles (Hieraaetus pennatus) and Implications for Management” (Journal of Applied Ecology, Vol. 37, pp. 215–223), the distances of such nests to the nearest marshland are normally distributed with mean 4.66 km and standard deviation 0.75 km. Let Y be the distance of a randomly selected nest to the nearest marshland. Determine and interpret
a. P(Y > 5).
b. P(3 ≤ Y ≤ 6).