What percentage of bags are rejected due to weight?

In summary, the conversation is about a statistics homework problem involving bags of sweets packed by a machine with a normal distribution. The bags are rejected if they are underweight (X < 225g) or overweight (X > 270g). The problem asks for the percentage of bags that are rejected. The solution involves using the normal distribution table to find the area under the curve for a given z-score. The conversation ends with the asker thanking the responder for their help.
  • #1
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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  • #2
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.
 
  • #3
"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
 
  • #5
Hi James,

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

Matt
 

Related to What percentage of bags are rejected due to weight?

1. What is a form of standard deviation?

A form of standard deviation is a statistical measure used to quantify the amount of variation or dispersion of a set of data values from the mean of the data set. It is often used to describe the spread of data points around the average value.

2. How is a form of standard deviation calculated?

A form of standard deviation is calculated by finding the square root of the sum of squared differences between each data point and the mean of the data set, divided by the number of data points in the set. This calculation can be done using a formula or with the help of software or a calculator.

3. What are the different types of standard deviation?

There are three main types of standard deviation: population standard deviation, sample standard deviation, and corrected sample standard deviation. Population standard deviation is used when the entire population is being considered, while sample standard deviation is used when a subset of the population, or sample, is being analyzed. Corrected sample standard deviation is used when the sample size is small and a more accurate estimate of the population standard deviation is needed.

4. How is standard deviation used in scientific research?

Standard deviation is commonly used in scientific research to assess the reliability of data and to compare the variability of different data sets. It is also used to identify outliers, or data points that are significantly different from the rest of the data, which can help researchers understand the underlying patterns and trends in the data.

5. Can standard deviation be negative?

No, standard deviation cannot be negative. It is a measure of dispersion, and therefore, it will always be a positive value. A value of zero indicates that all data points are identical, while a higher value indicates a larger spread of data points from the mean.

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