5.140 Statistics and Probability, Weight of corn chip bags

The net weight per bag of a certain brand of corn chips is listed as 10 ounces. The weight of chips actually dispensed is each bag by an automated machine, whenoperating to specifications, is a normal random variable with mean 10.5 ounces and standard deviation 0.25 ounce. A quality control inspector will randomly choose 1500bags from the automated process and measure the weight of each bag precisely. Ideally, all of the bags should contain at least 10 ounces of corn chips. However, if atleast 97% of the bags contain 10 ounces or more, the process is considered -under control- and no adjustments to the machine are deemed necessary. Assess thelikelihood that the quality control inspector will find fewer than 97% of the bags with 10 ounces or more even if the process is -under control-. Calculate.


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