Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 131 millimeters, and a standard deviation of 7 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 1.9 millimeters? Round your answer to four decimal places.

Answer: 0.1310Step-by-step explanation:Given : Mean : [tex]\mu = \text{131 millimeters}[/tex]Standard deviation :  [tex]\sigma = \text{7 millimeters}[/tex]Sample size : [tex]n=31[/tex]To find the probability that the sample mean would differ from the population mean by more than 1.9 millimeters i.e. less than 129.1 milliliters and less than 132.9 milliliters.The formula for z-score :-[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For x = 129.1 milliliters[tex]z=\dfrac{129.1-131}{\dfrac{7}{\sqrt{31}}}\approx-1.51[/tex]For x = 132.9 milliliters[tex]z=\dfrac{132.9-131}{\dfrac{7}{\sqrt{31}}}\approx1.51[/tex]The P-value= [tex]P(x<-1.51)+P(x>1.51)[/tex][tex]=2P(z>1.51)=2(1-P(z<1.15))\\=2(1-0.9344783)\\=0.1310434\approx0.1310[/tex]Hence, the required probability = 0.1310