Question

The diameter of a cylindrical shaft door hinge is normally distributed with a population mean of 12.8 mm and a standard deviation of 0.35 mm. The specifications on the shaft are 13 ± 0.15 mm. What proportion of shafts conforms to the specifications?

Answer 1

Given: = 12.8 mm, = 0.35 mm

To find the probability, we need to find the Z scores first.

Z = (X - )/ [/Sqrt(n)]. Since n = 1, Z = (X - )/

We need to find the shaft who's diameters are between 13 - 0.15 = 12.85 and 13 + 0.15 = 13.15

i.e P?(12.85 < X < 13.15) = P(X < 12.85) - P(X < 13.15)

For P(X < 13.15); Z = (13.15 – 12.8)/0.35 = 1

The probability for P(X < 13.15) = 0.8413

For P(X < 12.85); Z = (12.85 – 12.8)/0.35 = 0.14

The probability for P(X < 12.85) = 0.5557

Therefore the required probability = 0.8413 - 0.5557 = 0.2856

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