Hi How to calculate the variance of X-Y here where X-N(100,10) and Y-N(90,5) Should it be sigma^2=10^2+5^2=125 instead od merely adding Also in this question why we haven't calculated std dev in the form of sigma/sqrt(n)?
1. As per C.L.T. X bar ~ N ( mu, sigma^2 / n ) 2. Working in units of 1000 X~ N ( 100, 10^2) 3. Now distribution of X bar using (1.) X bar ~ N (100, 10^2 /10) i.e. N(100,10) 4. Same as the case for Y bar. 5. Thus we get Variance for X bar & Y bar 10 & 5 respectively and Variance of X bar - Y bar is simply sum of both i.e. 15. 6. and effectively we calculated in same way you mention.
Remember: A N(100,10) distribution => variance = 10 2nd part: You are confusing between a population result with a sample result. This is a population result and hence no need of a 'n'
