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Probability: ranges in Gaussian approximation

  1. Feb 7, 2006 #1
    Hello everyone,

    I got stuck on a probability question and would be very thankful if someone could give me a hint:

    An Opaque bag contains 10 green counters and 20 red. One couner is selected at random and then replaced: green scores 1 and red scores zero.

    1) Calculate the probability of obtaining scores in the ranges <r> +/- 0.5* root(var(x)) and <r> +/- root(var(x))

    that doesn't seem too bad. for the variance and the mean I got 2.22 and 1.66 respectively, so the ranges are:

    a) from 0.66 to 2.32, so I just add P(1) + P(2)= 0.67

    b) from .17 to 3.17, so this is P = P(1) + P(2) + P(3)= .823

    2) The Gaussian approximation of the binomial distribuion in (1) is given as P(r) = exp [-9(r-5/3)^2/20]; now do the same as in 1 and compare the answers. In what sense is P(r) a good approximation to p?

    OK, so I don't know how to go on from here. Help's very mcuh appreciated!
  2. jcsd
  3. Feb 8, 2006 #2
    Can anyone help?
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