A laundry detergent manufacturing industry produces a machine that fills boxes of laundry flakes. The machine is set for 16 oz net weight. The net weights of boxes filled from the machine have a mean of 16 oz and a standard deviation of 0.3 oz, and they are normally distributed.

a. What proportion of the boxes will have net weights of more than 15 oz?
b. What proportion of the boxes will have net weights of more than 16.5 oz?
c. What proportion of the boxes weights dliffering from the mean weight for all boxes by more than 0.4 oz? 2
d. If a sample of 32 boxes is drawn, what is the probability that its mean net weight will be greater than 16.3 oz?
e. If a sample of 32 boxes is drawn, what is the probability that its mean net weight will be less than 15.8 oz?