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Suppose X is a normally distributed random variable with the mean u(Mu) and variance sigma^2. Suppose P(X </= 10) - .6915 and P (X </= 20) -.8413. Find Mu and Sigma^2.


  • Statistics -

    for z-scores,
    z = (x - m)/s

    from my charts, a prob of .6915 corresponds to a z-score of .5
    so .5 = (10 - m)/s
    .5s = 10-m
    m = 10 - .5s

    and a prob of .8413 corresponds to a z-score of .9998 or 1
    1 = (20-m)/s
    s= 20-m
    m = 20 - s

    then 20 - s = 10 - .5s
    s = -10/-.5 = 20
    m = 0

    If I recall variance is the square of the standard deviation.

    I checked my answers with

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