1. A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 5 inches. A random sample of 32 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)
2. Assume that IQ scores are normally distributed, with a standard deviation of 18 points and a mean of 100 points. If 95 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points? (Round your answer to four decimal places.)