Question: Number 10 (#10) cans of peaches are supposed to contain 72 oz (according to the label.) The mechanism which controls the fills is initially set to produce a mean fill of 72.6 oz. However, the variability inherent in any machine causes the actual amounts to vary. The distribution of fills is normal and has a standard deviation of .4 oz.
A) How many out of 100,000 cans will have less than 72 oz?
B) The manufacturer feels that this is too many. Assuming the standard deviation remains unchanged, what mean should the manufacturer set if she wants no more than 300 of the cans to contain less than 72 oz?