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

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}=
`(x-0.95)/(1.05-0.95)`

=
`(x-0.95)/(0.1)`

b) P(X>1.02)= 1 - P(X≤1.02)

=
`1- (1.02-0.95)/(0.1)`

= 0.3

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

d) mean =
`(0.95+1.05)/(2)`

= 1

variance =
`((1.05-0.95)^2)/(12)`

= 0.000833