(a) Suppose Z is a standard normal random variable and let X = 32 1. (i) (2 points) Find Pr(1 g X g 1). (ii) (1 point) What is the probability that X is within one standard deviation of its mean? (iii) (4 points) Find the value of Pr{(X 1)2 > 1}. (b) The weights (in grams) of a population of mice fed on a certain diet since birth are assumed to be normally distributed with mean u = 100 and standard deviation 0 = 20. A random sample of n = 10 mice is taken from this population. (i) (4 points) Find the probability that at least two mice weigh between 75 and 90 grams. (ii) (2 points) Find the probability that the mean weight of the mice is greater than 110 grams