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Math Help - Normal distribution

  1. #1
    vicky86
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    Normal distribution

    Hi! I really, really need some help with a question on an assignment i have to do for quantitative analysis. The question is as follows: "What is the chance that a sample of 5 pies will have a mean less than 275 gm given the current machine setting?"
    The machine setting is to produce pies with a mean weight of 285 gms. The standard deviation is 5 gms and weights are normally distributed. The probability of one pie being under 275 gms is 2.28% and there are 12,000 pies in one group from which a sample is taken.
    Pleeeease could someone help me out with this?
    /Vicky
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by vicky86 View Post
    Hi! I really, really need some help with a question on an assignment i have to do for quantitative analysis. The question is as follows: "What is the chance that a sample of 5 pies will have a mean less than 275 gm given the current machine setting?"
    The machine setting is to produce pies with a mean weight of 285 gms. The standard deviation is 5 gms and weights are normally distributed. The probability of one pie being under 275 gms is 2.28% and there are 12,000 pies in one group from which a sample is taken.
    Pleeeease could someone help me out with this?
    /Vicky
    The mean m of a sample of size N taken from a population \sim N(\mu,\sigma^2) has a N(\mu,\sigma^2/N) distribution. Hence \overline{m}=\mu=285 and the standard deviation of m is \sigma/\sqrt{N}=\sqrt{5} So the z score corresponding to m=275 is:

    z=\frac{275-285}{\sqrt{5}}=10/\sqrt{5}\approx -4.47

    which is off the bottom of my normal distribution table so the reqired probability is essentialy 0.

    RonL
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