What percentage of bags are rejected due to weight?

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Homework Help Overview

The discussion revolves around a statistics homework question concerning the rejection rates of bags based on their weights, which are normally distributed with a specified mean and standard deviation. The problem specifically asks for the percentage of bags that are rejected for being underweight or overweight.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to approach the problem without a formula, questioning whether an altered version of the standard deviation formula could be applicable. Some participants suggest using z-scores and reference tables for the normal distribution to find the probabilities associated with the rejection criteria.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the use of z-scores and normal distribution tables. There is an ongoing exchange of clarification and support, with no explicit consensus reached yet.

Contextual Notes

The original poster expresses uncertainty about the calculations and the source of specific values related to the normal distribution, indicating a need for further exploration of statistical resources.

Matt.D
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*I have already posted this in another forum, but re-read the rules regarding homework questions.. Mods, I hope this is ok*

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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You don't need to calculate the standard deviation in this problem; it's given to you. You should have (either in your textbook or look it up on the net) a plot and table of the normal distribution. As far as I know, it's pretty standard to see the area under the curve from zero to a given z-score tabulated. The z-score is defined as the distance away from the mean as a fraction of the standard deviation ([tex]z = \frac{x-\bar x}{\sigma}[/tex]).

For your problem, you want to find the sum of the probability that a sample is higher than 270 and lower than 225. For a 270, the z-score is (270-250)/10 = 2 (that's how many standard deviations away from the mean it is). If you look up the area under the normal distribution for z = 2, you should get 0.47725 (unless I read off the wrong row or something). That means that ~48% of the data is between z = 0 and z = 2. But you want to know how much of the data is greater than z = 2, so your answer would be 50% - 0.47725 (because the total area under the curve from z = 0 to z = infinity is 50%, right?).

Now do the same thing for the lower rejection point and add the two probabilities together (and express your answer as a percentage).

I hope that gets you going with problems like this.
 
"If you look up the area under the normal distribution for z = 2, you should get 0.47725 (unless I read off the wrong row or something)"

Hi James,

Thanks for your help so far but I've become a little unstuck trying to find 0.47725? I don't understand where that comes from.

Regards

Matt
 
Hi James,

Thanks for all your help. I now understand Normal Distribution that little bit better :)

Matt
 

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