SOLUTION: 7d A grinding machine produces components with a mean diameter of 30 mm. All the components are measured and the actual size logged. The standard deviation over a period of time is
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Question 1063396: 7d A grinding machine produces components with a mean diameter of 30 mm. All the components are measured and the actual size logged. The standard deviation over a period of time is 0.05 mm. Assuming the normal distribution represents the actual distribution, what is the probability of a component being between 29.95 mm and 30.05 mm diameter?
You can put this solution on YOUR website! We use the normal distribution z-tables and the associated probability(P) to solve this problem
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P ( 29.95 < X < 30.05 ) = P ( X < 30.05 ) - P ( X < 29.95)
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z-value for 30.05 is (30.05 - 30.00) / 0.05 = 1, therefore
P ( X < 30.05 ) = 0.8413
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z-value for 29.95 is (29.95 - 30.00) / 0.05 = -1, therefore
P ( X < 29.95 ) = 0.1587
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P ( 29.95 < X < 30.05 ) = 0.8413 - 0.1587 = 0.6826
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