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Math Help - Probability of the mean of sample

  1. #1
    Yan
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    Probability of the mean of sample

    a random sample of size 100 is taken from a normal population with SD=25. what is the probability that the mean of the sample will differ from the mean of the population by 3 or more either way?

    I calculate it as
    P(mean of sample - mean >3)=P(Z>3/2.5)

    =P(Z>1.2)=0.1151, but the answer is different. can you tell me where did I get wrong?
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    a random sample of size 100 is taken from a normal population with SD=25. what is the probability that the mean of the sample will differ from the mean of the population by 3 or more either way?

    I calculate it as
    P(mean of sample - mean >3)=P(Z>3/2.5)

    =P(Z>1.2)=0.1151, but the answer is different. can you tell me where did I get wrong?
    |\overline{X} - \mu| > 3

     \Rightarrow \overline{X} > 3 + \mu or \overline{X} < -3 + \mu

     \Rightarrow Z > 1.2 or Z < -1.2.

    So the answer will be {\color{red}2} \Pr(Z > 1.2).
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