Question

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 368368 watts with a standard deviation of 1212 watts.

What is the probability that the mean amplifier output would be less than 365.6365.6 watts in a sample of 8484 amplifiers if the claim is true? Round your answer to four decimal places.

Answer 1

Given : u = 368,0= 12 and n=84 By Central Limit Theorem, ž follows a Normal distribution with mean = u = 368 standard error = 0/Vn = (12/184) = 1.3093 Then z=(x-mean)/SD = (x-368)/1.3093 follows standard Normal. When x=365.6, z=(365.6-368)/1.3093 = -1.83 P(Z<-1.83) =0.0336 [using Normal table or Excel : NORM.S.DIST(-1.83, TRUE)] Pi< 365.6) = P(Z < -1.83 ) = 0.0336