1. Consider a random sample X1, . . . , X35, El? N(p,02] of 35 observations from a normal distribution with known mean p, and known variance 0!. (a) 'What is the probability that the rst observation in the random sample is at least 3 standard deviations from the mean? {i.e., what is P(|X1 p| Z 30)?) {3 pts} (b) TWhat is the probability that at least one of the 35 observations is at least 3 standard deviations from the mean? (4 pts) (:3) Let Y denote the number of observations from the random sample that are at least 3 standard deviations from the mean. 'Nhat is the sampling distribution of Y? [4 pts} (d) What is the sampling distribution of IV 2 X1 X2? {4 pts}