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Homework answers / question archive / By law a box of cereal labeled as containing 16 ounces must contain at least 16 ounces of cereal
By law a box of cereal labeled as containing 16 ounces must contain at least 16 ounces of cereal. It is known that the machine filling the boxes produces a distribution of fill weights that is mound-shaped, with mean equal to the setting on the machine and with a standard deviation equal to .03 ounce. To ensure that most of the boxes contain at least 16 ounces, the machine is set so that the mean fill per box is 16.09 ounces. What percentage of the boxes do, in fact, contain at least 16 ounces? (Hint: Think normal distribution)
Answer: The machine's mean fill rate is set to 16.09 ounces. With the standard deviation of 0.03 ounces, this will assure that 99% or more of the boxes of cereal will weigh at least 16 ounce.
This is because the weight 16 ounces is 3 standard deviations below the mean, and from 3 standard deviations below the mean to 3 standard deviations above the mean represents represents at least 99% of the data in a normal distribution.
