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irinina [24]
2 years ago
6

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. Determine the foll

owing: (a) Cumulative distribution function of flange thickness (b) Proportion of flanges that exceeds 1.02 millimeters (c) Thickness exceeded by 90% of the flanges (d) Mean and variance of flange thickness
Mathematics
1 answer:
Mrrafil [7]2 years ago
4 0

Answer

given,

thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

X = U[0.95,1.05]           0.95≤ x ≤ 1.05

the cumulative distribution function of flange

F(x) = P{X≤ x}=\dfrac{x-0.95}{1.05-0.95}

                     =\dfrac{x-0.95}{0.1}

b) P(X>1.02)= 1 - P(X≤1.02)

                   = 1- \dfrac{1.02-0.95}{0.1}

                   = 0.3

c) The thickness greater than 0.96 exceeded by 90% of the flanges.

d) mean = \dfrac{0.95+1.05}{2}

              = 1

   variance = \dfrac{(1.05-0.95)^2}{12}

                  = 0.000833

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