Question

A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 89 months with a standard deviation of 5 months. If the claim is true, what is the probability that the mean monitor life would be less than 87.8 months in a sample of 123 monitors? Round your answer to four decimal places.

Answer 1

Answer: 0.0039

Step-by-step explanation:

Let x be a random variable that represents the mean life of computers .

As per given , we have

$\mu=89$ months

$\sigma=5$ months

sample size : n= 123

We assume that the mean life of new computers is approximately normally distributed.

∵ $z=\dfrac{x-\mu}\dfrac{{\sigma}{\sqrt{n}}}$

Then for x= 87.8

$z=\dfrac{87.8-89}{\dfrac{5}{\sqrt{123}}}=-2.66172876154\\\\\approx-2.66$  

The probability that the mean monitor life would be less than 87.8 months in a sample of 123 monitors :-

$P(x$

Hence, the probability that the mean monitor life would be less than 87.8 months in a sample of 123 monitors = 0.0039