Question 5. Aerospace Inspections The thickness of a flange on an aircraft compo

Question

Question 5. Aerospace Inspections The thickness of a flange on an aircraft component is Uniformly distributed between 0.9 and 1.1 millimetres. Determine the following (a) Cumulative distribution function of flange thickness. (b) Proportion of flanges that exceeds 1.02 millimetres. (c) Thickness exceeds 75% of the flanges. (d) Mean and standard deviation of flange thickness (e) Assume now that you are sampling 12 independent flanges. What is the variance of the number of flanges with a thickness less than 0.96 millimetres?

Explanation / Answer

a) here this is uniform distribution for paramter a =0.9 and b=1.1

CDF =P(X<x) =(x-a)/(b-a) =(x-0.9)/0.2 =5*(x-0.9)

b)P(X>1.02)=1-P(X<1.02)=1-1 =0 (As flange thickness are less than 1.1 )

c) at 75th percentile ; 0.75 =5*(x-0.9)

x =1.05

d)

mean =(a+b)/2 =(0.9+1.1)/2 =1

std deviation =(b-a)/(12)1/2 =0.0577

e) here probability of havng thickness less than 0.96 mm =P(X<0.96)=5*(0.96-0.9)=0.30

for probablity of thickness less than 0.96 mm is fixed and indepednent from compnent to component

therefore it follows binomial distribution with paramter n=12 ; p=0.30

variance =np(1-p) =12*0.3*(1-0.3) =2.52

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