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)
E(X) = 10 and Var(X) = 42 / 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?