Plastic strips that are used in a sensitive electronic device are manufactured t

Question

Plastic strips that are used in a sensitive electronic device are manufactured to a maximum specification of 305.70 mm (approximately 12.04 in) and a minimum specification of 304.55 mm (approximately 11.99 in). If the strips are less than the minimum specification, they are scrapped; if they are greater than the maximum specification, they are reworked. The part dimensions are normally distributed with a population mean of 305.20 mm (approximately 12.02 in) and a standard deviation of 0.25 mm. What is the expected percentage of scrap and rework?

Explanation / Answer

Given mean = 305.20

Standard Deviation = 0.25

For x = 305.70 inches

z = (305.70 - 305.20) / 0.25 = 2

y = 304.55 inches

z = (304.55 - 305.20) / 0.25 = -2.6

Hence P(304.55 < x < 305.70) = P(-2.6 < z < 2) = [area to the left of z = 2] - [area to the left of -2.6]

= 0.9772 - 0.0047 = 0.9725

Hence the expected percentage of scrap and rework = 97.25%

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