The thickness of a part is to have an upper specification of 0.925 and a lower specification of 0.870 mm. the average of the process is currently 0.917 with a standard deviation of 0.005. what is the probability that the product specification will be above 0.90 mm?

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Lilliana Hopkins

Mathematics

19 February, 11:39

The thickness of a part is to have an upper specification of 0.925 and a lower specification of 0.870 mm. the average of the process is currently 0.917 with a standard deviation of 0.005. what is the probability that the product specification will be above 0.90 mm?

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Gaven Jacobson · Answer 1

To solve this problem, we make use of the z statistic. The formula for the z score is:z score = (x - u) / swhere x is the sample value = 0.90, u is the sample mean = 0.917, and s is the standard deviation = 0.005

Therefore:z score = (0.90 - 0.917) / 0.005z score = - 3.4

From the standard probability tables, the p-value for a right tailed test of z = - 3.4 is:P = 0.9997

Therefore there is a 99.97% chance that it will be above 0.90 mm