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 and .

a. Compute E(X) and V(X).

m 5 5 s 5 .1 100(1 2 a)

z 100(1 2

a) a m

|

CV 5 .40 (CV 5 sX/mX)

X 5 0 , p , 1 a 5 1.817 b 5 .863

b. Compute .

c. Compute .

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?