Question: A machine in a catsup bottling plant is designed to dispense an average of 12 ounces per bottle, with a variance of 0.5 ounces.

a. If the machine is operating as designed, and if the distribution of amounts dispensed is relatively symmetric and mound-shaped, what is the proportion of bottles that can be expected to contain between 11.29 and 12.71 ounces?

b. If the machine is operating as designed, but the distribution of amounts dispensed is not symmetric or mound-shaped, what is the minimum proportion of bottles that can be expected to contain between 10.59 and 13.41 ounces?