A theoretical justification based on a certain material fail

A theoretical justification based on a certain material failure mechanism underlies the assumption that ductile strength X of a material has a lognormal distribution. Suppose the parameters are Mu = 5.0 sigma and = 0.09. (d) What is the value of median ductile strength? (Round your answer to three decimal places.) 148.41 (e) If ten different samples of an alloy steel of this type were subjected to a strength test, how many would you expect to have strength of at least 125? (Round your answer to three decimal places.) 9.83 X samples (f) If the smallest 5% of strength values were unacceptable, what would the minimum acceptable strength be? (Round your answer to three decimal places.) 72.O96

Solution

Mean of lognormal = E(X) = e^5-0.0081= 147.14

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Var= (e^0.0081-1)e^10.0081=176.06

std dev = 13.27

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e) P(X>=125) = 1-F(125) = 1-P(Z>(ln125-147.14)/0.09)

= 1-P(z>-10.72) =1-1 =0

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f) Smallest 5% strength is having z value = -1.64

ln x = 5+0.0081(-1.64)

=5-0.01328 = 4.987