A random sample of 40 men was selected from the residents of the central Bolivian city of Cochabamba and the men's weights were weighed. Below are the weights rounded to the nearest kilogram:

74 87 80 71 77 67 80 83 78 84 75 79 73 79 81 77 89 68 74 93 86 65 82 87 78 92 76 78 73 81 75 76 78 78 81 75 76 7883 M N = 40 Weight 78.40000 / Std.dev. 6.456164

Determine the 95% adult interval for the mean weight of men in Cochabambante, a) when it is assumed that the weight variance has been measured in previous studies 6.3245552^2 kg^2. b) the variance estimated on the basis of the sample is used ^2 = 6.4562^2 kg^2. c) What is the probability that the combined weight of eight randomly selected Cochabambinos (male residents of the city) exceeds the weight limit of the city elevator of 640 kg, assuming that the average weight is 78.4 kg and the variance of the weight is 6.3245552^2 kg^2.