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 μ = 5 and σ = .1.
a. Compute E ( X ) and V ( X ).
b. Compute P(X > 125).
c. ComputeP(110 ≤ X ≤ 125) .
d. What is the value of median ductile strength?
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?
f. If the smallest 5% of strength values were unacceptable, what would the minimum acceptable strength be?
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