Through process design improvements, the process standard deviation can be reduced to 0.04. Assume the process control remains the same, with weights less than 9.88 or greater than 10.12 ounces being classified as defects. Calculate the probability of a defect.

Complete Question

Assume a production process produces items with a mean weight of 10 ounces.

Through process design improvements, the process standard deviation can be reduced to 0.04. Assume the process control remains the same, with weights less than 9.88 or greater than 10.12 ounces being classified as defects. Calculate the probability of a defect.

0.0027

Step-by-step explanation:

We solve using the formula for z score

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 10 ounces

σ is the population standard deviation = 0.04 ounces

Hence:

For x < 9.88 ounces

z = 9.88 - 10/0.04

z = -3

Probability value from Z-Table:

P(x < 9.88) = 0.0013499

For x > 10.12 ounces

z = 10.12 - 10/0.04

z = 3

Probability value from Z-Table:

P(x<10.12) = 0.99865

P(x>10.12) = 1 - P(x<10.12)

= 0.0013499

The probability of a defect is calculated as:

P(x = 10.12) or P(x = 9.88)

P(z = 3) or P(z = -3)

= 2P

= 2(0.0013499)

= 0.0026998

Approximately = 0.0027

Therefore, the Probability of the defect is 0.0027

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