Question

An operation manager at an electronic company wants to test their amplifiers. The design engineer claims they have a mean output of 368 watts with a standard deviation of 12 watts. What is the probability that the mean amplifier output would differ from population mean by less than 3.8 watts in a sample of 84 amplifiers if the claim is true. Round answer to 4 decimal places

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	368
std deviation   =σ=	12.000
sample size       =n=	84
std error=σx̅=σ/√n=	1.30931

probability that the mean amplifier output would differ from population mean by less than 3.8 watts:

probability =P((-3.8)/1.309)<Z<(3.8)/1.309)=P(-2.9<Z<2.9)=0.9981-0.0019=0.9962