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Math Help - find sample mean and S.D

  1. #1
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    find sample mean and S.D

    Suppose a random sample of n=36 observations is selected from a population that has normal distribution with mean 106 and standard deviation 12.

    a) Give the mean and the standard deviation of the sample mean X bar.

    b) find the probability that X bar exceeds 108.

    c) Find the probability that the sample mean deviates from the population mean by less than 3.


    I dun quite understand part a and part c, isn't the sample mean same a the population mean? How about the standard deviation, which formula shud I use?

    For part b, I use P(X bar >= 108)= P(z>=108-106/(12/square root of 30)), is this correct?
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  2. #2
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    Re: find sample mean and S.D

    Part b) looks good but 36 is in the square root, not 30.

    For part a) \displaystyle \mu_{\bar{x}} = \mu , \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
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  3. #3
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    Re: find sample mean and S.D

    Quote Originally Posted by pickslides View Post
    Part b) looks good but 36 is in the square root, not 30.

    For part a) \displaystyle \mu_{\bar{x}} = \mu , \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
    thanks a lot, so for part c, do I just follow part b to find: P(z<3)=p(<=2)?
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