Consider an i.i.d. sample X 1 , ... , X n Poiss ( ) for > 0 . Starting from the Central Limit Theorem, find a confidence interval for of the form I = [ A , B ] with asymptotic level 1 that is centered about X n using the plug-in method. ( Write barX_n for X n . If applicable, type abs(x) for | x | , Phi(x) for ( x ) = P ( Z x ) where Z N ( 0 , 1 ) , and q(alpha) for q , the 1 quantile of a standard normal variable. )