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(STATISTICS) 3 randomly selected observations from standard norm dist

  1. Aug 12, 2013 #1
    1. The problem statement, all variables and given/known data

    3 randomly selected observations form the standard normal distribution are selected. What is the probability that their sum is less than 2?

    2. Relevant equations



    3. The attempt at a solution

    I know that the answer is 0.874928, but I don't know how to get that.


    In my mind, you would say that 2/3=0.67, so what is the probability that the average of the 3 values is less than 0.67?

    This gets me the wrong answer however.
     
  2. jcsd
  3. Aug 12, 2013 #2

    Simon Bridge

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    How do you add normal distributions?
     
  4. Aug 12, 2013 #3
    I think what the question is asking, is that 3 random numbers are chosen FROM a standard normal distribution. It's then asking what the chances are that their sum is less than 2.
     
  5. Aug 13, 2013 #4

    Simon Bridge

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    Same thing.
    The numbers are x,y, and z - their possible values are distributed normally with mean 0 and standard deviation 1.

    the sum of them is s=x+y+z ... s has a range of possible values too.
    You need to find how s is distributed, it's pdf, so you can find P(s<2). How do you add normal distributions?
     
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