A theoretical justification based on a certain material fail- ure mechanism underlies the assumption that ductile strength of a material has a lognormal distribution. Suppose the parameters are 5 and = .1.

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

b. Compute P(X > 125).

c. Compute P(110 x125).

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?