SOLUTION: The mean diameter of a CD disc is 12.0 cm, produced by a company called "Cardinal Best Compact Disk", with a standard deviation of 0.012. CD's that are more than one standard devia

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Question 384378: The mean diameter of a CD disc is 12.0 cm, produced by a company called "Cardinal Best Compact Disk", with a standard deviation of 0.012. CD's that are more than one standard deviation from the mean cannot be shipped. How can a quality control engineer use these statistics to help the company produce CD's that can be shipped?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that the diameters are normally distributed. The z-score formula is z+=+%28X+-+mu%29%2Fsigma, or vice-versa, X+=+mu+%2B+z%2Asigma. Within 1 sd, he can accept only diameter values within the interval [12.0 - 0.012, 12.0 + 0.012] = [11.988, 12.012]. There is 100% - 68.26% = 31.74% chance that a CD disc diameter is outside this interval. (The z-score tells us how many sd's X is away from mu.)