What Percentage of Bags Are Rejected Due to Weight Limits?

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SUMMARY

The discussion centers on calculating the percentage of bags rejected due to weight limits based on a normal distribution of bag weights. The mean weight is 250g with a standard deviation of 10g. Bags are rejected if they weigh less than 225g or more than 270g, which corresponds to 2.5 standard deviations below the mean and 2.0 standard deviations above the mean, respectively. Participants recommend using a normal distribution table to find the rejection percentages accurately.

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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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