By law, a box of cereal labeled as containing 20 ounces must contain at least 20

Question

By law, a box of cereal labeled as containing 20 ounces must contain at least 20 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 20 ounces, the machine is set so that the mean fill per box is 20.09 ounces. Assuming nothing is known about the shape of the distribution, what can be sald about the proportion of cereal boxes that contain less than 20 ounces. A. O B. ° C. O D. The proportion is less than 2.5%. The proportion is at most 5.5%. The proportion is at least 89%. The proportion is at most 11%.

Explanation / Answer

answer

mean is given as 20.09 and standard deviation given is 0.03

so, it is clear that 20 ounces is 3 standard deviation below the mean of 20.09

and using the normal distribution that approximately 99.97% values lie within 20 to 20.18

so, we can assume that the proportion is at least 89% because its the nearest value of 99.7%

option C is correct.

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