Scenario: A batch of precision aluminum fuel tank vent cover components have arr

Question

Scenario: A batch of precision aluminum fuel tank vent cover components have arrived to service a variety of engineering systems. A component is classed as defective if it has a diameter less than 69mm. In a batch of 350 components, the mean diameter is 75mm and the standard deviation is 2.8mm. Assuming that the diameters are normally distributed, determine how many are likely to be classed as defective. If those having a diameter of more than 81.5mm are to be rejected, then find, correct to the nearest component, the number likely to be rejected because of being oversized.

Explanation / Answer

Solution :-

a) Given, Mean diameter, x = 75 mm

Standard deviation, = 2.8 mm

= 69mm

Cumulative probability: P(X < 69) = 0.01606

we can find this by calculating z score, using, z = (X - ) /

Here, z = (75 - 69) / 2.8 = 2.14

Using z to p converter P (x < 69) = 0.016

1.62% of 350 components are likely to be rejected that is approximately 6.

b) Given, Mean diameter, x = 75 mm

Standard deviation, = 2.8 mm

= 81.5 mm

z = (75 - 81.5) / 2.8 = -2.32

Calculating P (x > 81.5) = 0.01013

or 1.013% of 350 are likely to be rejected which is approximately 4.

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