1. [20 points] A certain species of blue butterflies has an average mass of 405 mg with a standard deviation of 38 mg. Assume the masses are normally distributed. (a) A blue butterfly from the species is found to have mass 355 mg. What is the Z-score for its mass? (b) What is the meaning of the Z-score from (a)? (c) Find and interpret the percentile of the mass of the blue butterfly in (a). (d) What is the probability a randomly chosen butterfly from the species will have mass between 390 mg and 425 mg?