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Math Help - Sampling

  1. #1
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    Sampling

    The mean of a random sample of n observations drawn from an N(\mu , \sigma^2) distribution is denoted by \bar{x}. Given that P(| \bar{x} - \mu | < 0.5\sigma) < 0.05

    Find the smallest value of n.


    The only thing I can see to do is divide both sides of the inequality inside the bracket by \sigma to make it look like a normal distribution, but I can't see where to go from there.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by alrightgeez View Post
    The mean of a random sample of n observations drawn from an N(\mu , \sigma^2) distribution is denoted by \bar{x}. Given that P(| \bar{x} - \mu | < 0.5\sigma) < 0.05

    Find the smallest value of n.


    The only thing I can see to do is divide both sides of the inequality inside the bracket by \sigma to make it look like a normal distribution, but I can't see where to go from there.
    You need to use:

    \bar{x} \sim N(\mu,\sigma^2/n)

    CB
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