1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A form of standard deviation?

  1. Jan 16, 2005 #1
    *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 web site 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
     
  2. jcsd
  3. Jan 16, 2005 #2

    jamesrc

    User Avatar
    Science Advisor
    Gold Member

    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.
     
  4. Jan 17, 2005 #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. Jan 17, 2005 #4

    jamesrc

    User Avatar
    Science Advisor
    Gold Member

  6. Jan 19, 2005 #5
    Hi James,

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

    Matt
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A form of standard deviation?
  1. Standard Deviation (Replies: 2)

  2. Standard deviation (Replies: 6)

Loading...