81. 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
5 and
.1.

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

b. Compute P(X 125).

c. Compute P(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?