- #1
bonfire09
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Homework Statement
There are 55 independent normal observations with mean 100. The first 50 observations have variance 76.4 and last five have variance 127.
Calculate the probability that ##\bar{x}=\frac{1}{55}\sum_{i=1}^{55} X_i## is between 98 and 103.
Homework Equations
The Attempt at a Solution
The trouble I am having is finding the standard deviation of ##\bar{x}##.
What I did so far is Var(##\frac{1}{55}\sum_{i=1}^{55} X_i##)=##\frac{1}{55^2} Var(\sum_{i=1}^{55} X_i)=\frac{1}{55^2}[Var(X_1)+...+Var(X_{55})]= \frac{1}{55^2}*[76.4*50+127*5]=1.47272##. So the standard deviation of ##\bar{x}## is 1.213559.
Not sure if this correct or not?