What Percentage of Bags Are Rejected Due to Weight Limits?

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To determine the percentage of bags rejected due to weight limits, the normal distribution of bag weights must be analyzed. The mean weight is 250g with a standard deviation of 10g, leading to rejection thresholds at 225g for underweight and 270g for overweight. Underweight bags fall 2.5 standard deviations below the mean, while overweight bags are 2.0 standard deviations above. Consulting a normal distribution table will provide the necessary values to calculate the rejection percentages. This approach will yield the total percentage of bags that are rejected based on the specified weight limits.
Matt.D
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Hey guys, I've got this question from my Statistics Homework and wondered if someone could point me to a website or supply some advice as to how to begin to solve the problem.


Bags of sweets are packed by a machine such that the masses (X) have a normal distribution with mean 250g and standard deviation 10g.
A bag is judged to be underweight and rejected if X<225g.
A bag is judged to be overweight and rejected if X>270g
What percentage of bags are rejected?

I've tried a few combinations, but without a formula I don't think I'm making any sense. Can an altered version of the formula for Standard Deviation be used?

Any help always appreciated : )

Matt
 
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Underweight is 2.5 s.d. too low, while overweight is 2.0 s.d. too high. Look up a table of values for the normal distribution (not the density function, which is the bell curve).
 

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