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Sampling distribution of sample mean

  1. May 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Let X1,X2,...X10 be independent normal random variables with mean 10 and std dev 4. Let Y = X1+X2+...+X10. Let X be Y/10. What is P(X < 8)


    2. Relevant equations
    E(X) = 10 and Var(X) = 42 / 10 = 1.6
    std dev of X = 1.6.5 = 1.26


    3. The attempt at a solution

    To convert to standard normal distribution to use z table to solve I get..

    P(X-10/1.26 < (8-10)/1.26) = P(Z < -1.58) = 0

    I really doubt that I have done this problem correctly because it is on a sample exam and seems too easy. Have I done anything incorrectly or am I just second guessing myself needlessly?
     
  2. jcsd
  3. May 7, 2009 #2
    Just the typo in the last line where you say the probability is 0.

    Yes!
     
  4. May 8, 2009 #3
    Ah. A silly mental error as I was using an applet to find the value for z that matched the probability but with a curve that had the mean and standard deviation of the original variable. Thanks for helping me again Billy Bob!
     
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