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Math Help - normally distributed

  1. #1
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    normally distributed

    If X is normally distributed with mean 40 and standard deviation of 0.8 , find the value of a such that

    (1) P ( | X-40 | < a ) = 0.7521


    (2) P ( | X-40 ) > a ) = 0.2812


    Can someone pls show me the steps and what does it mean when modulus is applied to the variable X ?
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    If X is normally distributed with mean 40 and standard deviation of 0.8 , find the value of a such that

    (1) P ( | X-40 | < a ) = 0.7521


    (2) P ( | X-40 ) > a ) = 0.2812


    Can someone pls show me the steps and what does it mean when modulus is applied to the variable X ?
    (1) \Pr( |X - 40| < a) = \Pr(-a < X - 40 < a) = \Pr(-a + 40 < X < a + 40) = 1 - 2 \Pr(X < a + 40) by symmetry.

    Therefore \Pr(X < a + 40) = \frac{1 - 0.7521}{2} = .....

    This has the form Pr( X < x*) = number, which is a type of question you should know how to do.


    (2) \Pr( |X - 40| > a) = \Pr(X - 40 > a) + \Pr(X - 40 < -a) = 2 \Pr(X - 40 < -a) = 2 \Pr(X < -a + 40) by symmetry.

    Therefore \Pr(X < -a + 40) = \frac{0.2812}{2} = .... which is again a type of question you should know how to do.
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  3. #3
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    Re :

    thank u very much mr fantastic for clearing my doubts .
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