Answer :
The probability that the sample mean would differ from the population mean by less than 0.5 millimeters is 0.3970.
Given mean diameter of 145 millimeters, standard deviation of 6 millimeters.
We have to find out the probability that the sample mean would differ from the population mean by less than 0.5 millimeters.
μ=145 and ,σ=60 ,n=39 then
s=60/[tex]\sqrt{39}[/tex]=0.96
By finding the probability that the sample mean would differ by less than 0.5 mm equal to p value of Z when X=145+0.5=145.5 mm subtracted by the p value of Z when X==145-0.5=144.5 mm.
When X=145.5 mm
Z=(X-μ)/σ
By central limit theorem
Z=(145.5-145)/5
=0.5/0.96
=0.52
p value of 0.52=0.6985.
When X=144.5
Z=(144.5-145)/0.96
=-0.5/0.96
=-0.52
p value of -0.52=0.5-0.1985=0.3015
Required probability=0.6985-0.3015=0.3970.
Hence the probability that the sample mean would differ from the population mean by less than 0.5 mm is 0.3970.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4