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## Homework Statement

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)

## Homework Equations

E(

__X__) = 10 and Var(

__X__) = 4

^{2}/ 10 = 1.6

std dev of

__X__= 1.6

^{.5}= 1.26

## 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?