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Probability and standard deviation Question

  1. Aug 11, 2015 #1
    1. The problem statement, all variables and given/known data
    A business owner makes jars with weights that follow a normal distribution with a standard deviation of 8 pounds. In a random sample of 64 jars what is the probability that the sample mean differs from the population mean by no more than 1 pound?

    2. Relevant equations
    ##z=\frac{x-\bar{x}}{\frac{\sigma}{\sqrt{n}}}##

    3. The attempt at a solution
    n=64
    ##\sigma##=8
    mean=##b##
    ##z_{2}=\frac{(b+1)-b}{\frac{8}{\sqrt{64}}}=0.125##
    ##z_{1}=\frac{(b-1)-b}{\frac{8}{\sqrt{64}}}=-0.125##
    ##P(-0.125<z<0.125)=P(z<0.125)-P(z<-0.125)=0.1232##
    Not really sure what I'm doing wrong here but this is not even close to the correct answer.
    Edit: Well this is really embarrassing I did the actual arithmetic wrong lol its 1/1 and -1/1 not 1/8 and -1/8
     
    Last edited: Aug 11, 2015
  2. jcsd
  3. Aug 15, 2015 #2

    Mark44

    Staff: Mentor

    So you have been able to figure this out?
     
  4. Aug 16, 2015 #3
    Yea I just messed up the arithmetic so that was giving me the wrong Z values.
     
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