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Math Help - What is the mean in this problem?

  1. #1
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    What is the mean in this problem?

    In a particular basketball league, the standard deviation in the distribution
    of players' height is 2 inches. Twenty- five players are selected at random
    and their heights are measured. Give an estimate for the probability that
    the average height of the players in this sample of 25 is within 1 inch of the
    league average height

    This is a central limit theorem problem.Here variance of 25 players = (S.D.)^2/n
    =4/25
    and therefore S.D. of 25 players = 2/5

    but what about mean ????

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  2. #2
    MHF Contributor
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    you dont need to know the population mean to answer this problem.

     \bar{X} \sim N(\mu, \frac{\sigma^2}{n})

     \bar{X} - \mu \sim N(0, \frac{\sigma^2}{n})


    You want to find

    \mathbb{P} ( \mu -1 \leq \bar{X} \leq \mu + 1 )

    But this is just:
    \mathbb{P} ( -1 \leq \bar{X} - \mu \leq 1 )


    You know the distribution of \bar{X} - \mu. Can you finish from there?


    If not...additional hint in spoiler
    Spoiler:

    This is just

     \mathbb{P} (-1 \leq Y \leq 1)

    where  Y \sim N(0,\frac{\sigma^2}{n})
    Last edited by SpringFan25; July 6th 2010 at 01:26 PM.
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  3. #3
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    Jun 2010
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    Thanks...I will solve it further...
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