5 Due: Monday, November 24th6th to the eginning of the LECTURE to the of the LECTURE Friday, April 17th to the beginning b beginning of the LECTURE Due: Friday, November 1. Weights of men in one age group are normally distributed with a standard deviation (!) of 9 lb. A researcher wishes to estimate the mean weight of all men in this age group. Find how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 2.96 lb. 2. In a poll taken to estimate the Prime Minister's current popularity, a random sample of 1000 voters was taken, and 59% of them responded that he is doing a good job. Construct a 95% confidence interval for the population proportion who think that way. 3. The restaurant in a large commercial building provides coffee for the building's occupants. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of 0.6. A new tenant of the building intends to have a total of 125 new employees. What is the probability that the new employees will consume more than 240 cups