A factory produces plate glass with a mean thickness of 4 mm and a standard deviation
of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured and the mean thickness of the 100 sheets is to be computed.

What is the probability that the average thickness of the 100 sheets is less than 4.1 mm?

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JeanaShupp JeanaShupp · Answer 1 · 2019-10-31T07:58:45+01:00

Answer: 0.5363

Step-by-step explanation:

Given : Population mean : [tex]\mu=4[/tex]

and standard deviation : [tex]\sigma=1.1[/tex]

sample size : n= 100

Let x be the random variable that represents the thickness of sheet.

Since the probability for each element in a Simple random sample is equal.

∴ Using formula [tex]z=\dfrac{x-\mu}\sigma}[/tex] ,

The z-value corresponds to x=4.1

[tex]z=\dfrac{4.1-4}{1.1}\approx0.091[/tex]

The probability that the sample mean would be greater than 139.7 millimeters will be :-

[tex]P(x<4.1)=P(z<0.091)= 0.5362537\approx0.5363[/tex]

Hence, the required probability : 0.5363