An automated filling machine fills soft-drink cans, and the standard deviation is 0.5 fluid ounce. Assume that the fill volumes of the cans are independent, normal random variables.

a. What is the standard deviation of the average fill volume of 100 cans?

b. If the mean fill volume is 12.1 oz, what is the probability that the average fill volume of 100 cans is less than 12 oz?

c. What should the mean fill volume equal so that the probability that the average of 100 cans is less than 12 oz is 0.005?

d. If the mean fill volume is 12.1 oz, what should the standard deviation of fill volume equal so that the probability that the average of 100 cans is less than 12 oz is 0.005?

e. Determine the number of cans that need to be measured such that the probability that the average fill volume is less than 12 oz is 0.01