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Homework Help: Probability Question - Nonstandard Normal Distributions

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known dataThe weight of eggs produced by a certain type of hen varies according to a distribution that is approximately normal with mean 6.5 grams and standard deviation 2 grams.

    What is the probability that the average of a random sample of the weights of 25 eggs will be less than 6 grams



    2. Relevant equations
    P(X<6)=P((6-6.5)/σ)



    3. The attempt at a solution - The part I can't figure out is how to arrive at sigma. This is a problem from a practice exam, so I already know that sigma is 0.40. If I'm understanding correctly, then that would make V(X) = 4/25. I just can't figure out how to arrive at these conclusion from the data that is given. I'm pretty stumped.
     
    Last edited: Mar 10, 2010
  2. jcsd
  3. Mar 10, 2010 #2

    statdad

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    Homework Helper

    your problem asks about the probability the MEAN of a sample will be a certain size. what do you know about distributions of sample means?
     
  4. Mar 10, 2010 #3
    Not much.

    I think I figured out why sigma is what it is though. Since the SD is 2 grams, it follows that V(X) = 4. Since I'm trying to find out what the average of X is, I divide 4 by 25. that is how I get the 4/25. From there sigma is easy. I think that is kind of close anyway.
     
    Last edited: Mar 10, 2010
  5. Mar 10, 2010 #4

    statdad

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    Homework Helper

    You've essentially got it. If you take a sample of size [tex] n [/tex] from a normally distributed population, then [tex] \overline X [/tex] has a normal distribution. For the
    distribution of [tex] \overline X [/tex],

    [tex]
    \mu = \text{ original population mean}
    [/tex]

    and

    [tex]
    \sigma = \frac{\text{Original standard deviation}}{\sqrt n}
    [/tex]

    As long as the original population itself has a normal distribution, this is true
    for any sample size.
     
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