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Math Help - Standard normal R.V. question

  1. #1
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    Standard normal R.V. question

    Let Z be the standard normal random variable. If z>0 and P(Z<=z) = a , what are P[Z<=(-z)] and P(-z<Z<z) ?

    <= is supposed to mean less than or equal to, I just didn't know how to type that

    I know that the answers are 1-a, and 2a-1. I just can't figure out how to show this.
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  2. #2
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    Quote Originally Posted by babbagandu View Post
    Let Z be the standard normal random variable. If z>0 and P(Z<=z) = a , what are P[Z<=(-z)] and P(-z<Z<z) ?

    <= is supposed to mean less than or equal to, I just didn't know how to type that

    I know that the answers are 1-a, and 2a-1. I just can't figure out how to show this.
    Draw pictures!!

    By symmetry, \Pr(Z \leq -z) = \Pr(Z \geq z) = 1 - a.

    \Pr(-z \leq Z \leq z) = 1 - \Pr(Z \leq -z) - \Pr(Z \geq z).
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