PVC pipe is manufactured with mean diameter of 1.01 inch and a standard deviation of 0.003 inch. Find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.

Answer: 0.8186Step-by-step explanation:Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]Standard deviation :  [tex]\sigma=0.003\text{ inch}[/tex]Sample size :  [tex]n=9[/tex]The formula to calculate z-score :-[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For x=1.009 inch[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]For x=1.012 inch[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]Hence, the required probability = 0.8186