Opisthotrochopodus n. sp. is a polychaete worm that inhabits deep-sea hydrothermal vents along the Mid-Atlantic Ridge. According to the article “Reproductive Biology of Free-Living and Commensal Polynoid Polychaetes at the Lucky Strike Hydrothermal Vent Field (Mid-Atlantic Ridge)” (Marine Ecology Progress Series, Vol. 181, pp. 201–214) by C. Van Dover et al., the lengths of female polychaete worms are normally distributed with mean 6.1 mm and standard deviation 1.3 mm. Let X denote the length of a randomly selected female polychaete worm. Determine and interpret
a. P(X ≤ 3).
b. P(5 < X < 7).