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.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-05T06:13:25+01:00

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

[tex]\mu=89[/tex] months

[tex]\sigma=5[/tex] months

sample size : n= 123

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

∵ [tex]z=\dfrac{x-\mu}\dfrac{{\sigma}{\sqrt{n}}}[/tex]

Then for x= 87.8

[tex]z=\dfrac{87.8-89}{\dfrac{5}{\sqrt{123}}}=-2.66172876154\\\\\approx-2.66[/tex]

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

[tex]P(x<87.8)=P(z<-2.66)=1-P(z<2.66)\\\\=1-0.9960929=0.0039071\approx0.0039[/tex]

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