I. The lognormal distribution is frequently used as a model for various material
ID: 3340884 • Letter: I
Question
I. The lognormal distribution is frequently used as a model for various material properties. The article "Reliability of Wood Joist Floor Systems with Creep (Journal of Structural Engineering) suggests that the lognormal distribution with 1nx-0.375 and 1x-0.25 is a plausible model for X the modulus of elasticity (MOE) of wood joist floor systems constructed from #2 grade hem-fir. Determine a. The probability that the MOE is between 1 and 2. b. What value of MOE represents the 99th percentile of this distribution? In other words what value of MOE is such that only 1% of all systems have an MOE exceeding that value?Explanation / Answer
a) here with above parameter : for lognormal distribution: z score =(ln(x)-mean)/std deviation=(ln(x)-0.375)/0.25
hence probability that MOE is between 1 and 2 =P(1<X<2) =P((ln(2)-0.375)/0.25<Z<(ln(1)-0.375)/0.25)
=P(-1.5<Z<1.2726)=0.8984-0.0668 =0.8316
b)
here for 99th percentile ; z score =2.326
hence corresponding value of MOE : x =emean+z*std deviation =e0.375+2.326*0.25 =e0.9566=2.6028
please revert for any explanation required.