Question

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

Answer 1

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