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Math Help - Central Limit Theorem

  1. #1
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    Central Limit Theorem

    See Question 3 on the attached document....

    It is a past exam paper but the solutions are not provided so i cant see where i am going wrong....

    I derived the PGF in part (i) then proceeded to get E(x) as 11/5 and Var(x) = 39/25

    The problem is in part (iii) in the central limit theorem. I constructed the sample mean as (11/5)*50 to give 110 and the variance as {\frac {\sigma}{\sqrt {n}}} which i got as such a small value (sqrt39/25)/(sqrt50) that it made my Z values so large that phi of these values were like 56 and -320 which would obviously be approximately 1-0, meaning almost the whole of the set is in this interval.... anyway it didnt seem right! have i gone wrong somewhere?
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  2. #2
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    Have i gone wrong on part (iii)?
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  3. #3
    MHF Contributor matheagle's Avatar
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    I'm not sure what you're asking.

    I get E(X)=2.2 and E(X^2)=6.4

    So V(X)=1.56

    Thus Y\approx N((50)(2.2), (50)(1.56))

    Since the X's are integer based you may want to put in a correction factor, but that won't
    alter your answer a whole lot.
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