1. (10 points) Compute the probabilities P[zsl.63)= P[z>1.37)= 2. Let x be a random variable representing the weight, in pounds, of a sh in a lake. You may assume that x has a normal distribution with mean pi = 3.1 and standard deviation 0' = 0.43. a. (10 points) Find the probability that a randomly caught fish weighs at least 4 pounds. b. (10 points) Find the probability that a random sample of n=40 fish has mean weight not more than 3 pounds. 3. (20 points) The average resting heart rate, in beats per minute, for a healthy adult male is [1:80. John is an adult male, and his doctor is concerned that .Iohn's heart rate is elevated. A random sample of n=17 of John's resting heart rates has mean rate 7?: 96. Let x be a random variable that represents John's resting heart rate. You may assume that x has an approximately normal distribution with standard deviation 0 = 20. Does the above sample result provide strong evidence that John's heart rate is elevated? Use a 0L=5% level of significance