Question 1: As part of his review for a chemistry test, a student randomly selects (without replacement) 40 out of 102 elements listed on the standard tables, and tries to guess their atomic numbers. Given that the mean of all 102 atomic numbers is 51.794, and the population standard deviation is 29.804, what is the probability that the mean of the 40 atomic numbers selected by the student will be at least 58.3?
Question 2: A random sample of 250 Ontario households using natural gas heating show that the mean monthly consumption of natural gas is 107.73 cu. ft., with a standard deviation of 13.94 cu. ft. Use these statistics to construct a 94% confidence interval for the mean monthly consumption for the population of all Ontario households.