Question

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 495495 watts with a standard deviation of 1212 watts.

What is the probability that the mean amplifier output would differ from the population mean by more than 1.91.9 watts in a sample of 8888 amplifiers if the claim is true? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 495

standard deviation = = 12

n = 88

=   = 495

= / n = 12 / 88 = 2.28

495 ± 1.9 = 493.1, 496.9

P(493.1 < < 496.9)  

= 1 - P[(493.1 - 495) / 2.28 < ( - ) / < (496.9 - 495) / 2.28)]

= 1 - P( - 0.83 < Z < 0.83 )

= 1 - P(Z < 0.83) - P(Z < - 0.83)

Using z table,  

= 1 - P( 0.7967 - 0.2033)   

= 1 - 0.5934

= 0.4066