P(251.63)= P(z>1.3'7]= 2. Let x be a random variable representing the weight, in pounds, of a fish in a lake. You may assume that x has a normal distribution with mean u = 3.1 and standard deviation or = 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 ,u=80. John is an adult male, and his doctor is concerned that John's heart rate is elevated. A random sample of n=17 of John's resting heart rates has mean rate at" = 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 or = 20. Does the above sample result provide strong evidence that John's heart rate is elevated? Use a o.=5% level of significance