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    It is given that X-N(50.0,8^2). The mean of 20 random observations of
    x is denoted by x̄. Find p( x̄>47).

    The part I was stuck on was when you approximate it to the normal distribution 47-50/√8^2-20 is used. I was confused on why √8^2-20 is used. Thanks in advance.
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    (Original post by Butterflyshy)
    It is given that X-N(50.0,8^2). The mean of 20 random observations of
    x is denoted by x̄. Find p( x̄>47).

    The part I was stuck on was when you approximate it to the normal distribution 47-50/√8^2-20 is used. I was confused on why √8^2-20 is used. Thanks in advance.
    This looks incorrect - there should be no minus 20.

    The distribution of the sample mean would be \bar{X}\sim N(50.0, \frac{8^2}{20})

    Is it perhaps a division, misprinted?
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    (Original post by ghostwalker)
    This looks incorrect - there should be no minus 20.

    The distribution of the sample mean would be \bar{X}\sim N(50.0, \frac{8^2}{20})

    Is it perhaps a division, misprinted?
    It is a division, sorry.
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    (Original post by Butterflyshy)
    It is a division, sorry.
    I presume you're OK with it now then. If not, what bit don't you follow.
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    (Original post by ghostwalker)
    I presme you're OK with it now then. If not, what bit don't you follow.
    I don't understand why you use √8^2/20
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    (Original post by Butterflyshy)
    I don't understand why you use √8^2/20
    The question asks you to find the probability that the sample mean is > 47. For that you need the distribution of the sample mean, which for a r.v. distrubuted N(\mu,\sigma^2) is N(\mu,\frac{\sigma^2}{n}), where n is the sample size.

    The standard deviation is then \frac{\sigma}{\sqrt{n}}
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    (Original post by ghostwalker)
    The question asks you to find the probability that the sample mean is > 47. For that you need the distribution of the sample mean, which for a r.v. distrubuted N(\mu,\sigma^2) is N(\mu,\frac{\sigma^2}{n}), where n is the sample size.

    The standard deviation is then \frac{\sigma}{\sqrt{n}}
    That makes sense
 
 
 
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