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2 years ago

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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

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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