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Stat HW: Xbar and sampling infinite populations

  1. Mar 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Two problems:
    1) We're given a probability distribution function with possible values and their probabilities of occurring:

    X=1, P = .67
    X=2, P = .19
    X=3, P = .05
    X=4, P = .04
    X=5, P = .03
    X=6, P = .02

    And we need to find P(XBAR >=6) and P(XBAR >=5). I don't get this XBAR business...

    2) Use Central Limit Theorem. Infinite population. 25% of the pop has the value 1, 25% 2, 25% 3, and 25% 4. What is the pop mean, pop std dev, sample mean, and sample std dev?

    2. Relevant equations

    1) I found that mu = E(X) = 1.69, variance = 1.494, std dev = 1.222, so mu of XBAR = 1.69 too, and std dev XBAR = stddev/(sqrt(n)) = .5

    So I figure you must need to get the Z statistic for XBAR, right? That must mean

    P(Xbar >=6) =

    P(x=6) =

    (Xbar - mu of XBAR)/(stddev of XBAR) =

    6 - 1.69/.5

    however, this value is too big for the Z / normal distribution table I've been given. What do I do about the Xbar crap?

    Same for the XBAR >= 5, the Z value is too big...

    2) The pop and sample mean are both 2.5, but shouldn't the std dev for an infinite pop be 0?

    3. The attempt at a solution
    See above.

    Thanks.
     
  2. jcsd
  3. Mar 21, 2013 #2

    SteamKing

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    xbar is the mean value of x (when printed, the x has a horizontal bar on top)
     
  4. Mar 21, 2013 #3
    ^No, because the mean (as I calculated) is 1.69. That's clearly always lower than 6 or 5.

    Anyone else?
     
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