Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ~ N (85,25)).
a. Let W = aX + b for some constants a, b notequalto 0. Write an expression for the pdf of W.
b. Suppose that X represents an approximate distribution of the final scores in a certain EENG course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the professor were to "curve" the scores, it means she would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose she wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should she choose for a and b? What students would see their score lowered, and what students would see their score increased?