Question

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 495 watts with a standard deviation of 12 watts. What is the probability that the mean amplifier output would differ from the population mean by less than 1.9 watts in a sample of 88 amplifiers if the claim is true? Round your answer to four decimal places.

Answer 1

Let's write the given information

sample size = n = 88

Let X is a random variable with mean 495 and standard deviation 12

For large n ( sample size), the distribution of sample mean is approximately normal ( By central limit theorem) With mean = 495

and standard deviation is as follows:

Here we want to find  

= P(Z < 1.4853) - P(Z < - 1.4853) ...( 1 )

Let's use excel:

P(Z < 1.4853) = "=NORMSDIST(1.4853)" = 0.9313

P(Z < - 1.4853) = "=NORMSDIST(-1.4853)" = 0.0687

Plug these values in equation ( 1 ), we get

So final answer is 0.8626