Question

Question: If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness?

Short answer

Answer

There is a requirement to first set up the probability of thickness of the washer = 2.4mm.

Step-by-step solution

  Finding out the value of Z 

Step 1: Finding out the value of Z

Value of Z =?

Formula = Sample mean + Z * Sample standard deviation = 2.4

Sample mean = 1.9625

Sample standard deviation = 0.2096

Z =?

Therefore, 1.9625 + Z * 0.2096 = 2.4

1.9625 + 0.2096.Z = 2.4 …..(1)

0.2096. Z = 1.9625 - 2.4

0.2096. Z = 0.4375 ………… (2)

Z = 0.4375 / 0.2096………… (3)

Z = 2.0873

 Fraction of the output is expected to be greater than the thickness

Step 2: Fraction of the output is expected to be greater than the thickness

Accordingly, the probability of thickness of 2.4mm or less is 0.9816.

As a result, the chance of a thickness greater than 2.4 mm is 1 - 0.9816 = 0.0184.

As a result, 0.0184 percent of output should be larger than 2.4 mm.

The fraction of output is expected to be higher than 2.4 mm is 0.0184.