Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. a] What is the probability that X 59? |:] c) What is the probability that all of the 180 measurements are greater than 59? :] d) What is the expected value of S? |:] e) What is the standard deviation of S? |:] f) What is the probability that s-1so*55 >10? :] 9) What is the standard deviation of 8-180*65 :I h) What is the expected value of M? :] i) What is the standard deviation of M? E j) What is the probability that M >65.41? :] k) What is the standard deviation of 180*M? :] I) If the probability of x > k is equal to .3, then what is k? |:]