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Problem 3 [12 Points]: The average height of a woman is increasing from 1960 to 2002. The average height of a woman aged 2074 years is 160 cm in 2002. Suppose the height of a woman is normally distributed with a standard deviation of 10 cm. (a) [4 points] What is the probability a randomly selected woman in this population is between 135 cm and 185 cm? (b) [4 points] What are the quartiles of this distribution? (c) [4 points] Determine a and b, which is symmetric about the mean and Pr(a