Recently, they have had some problems with their steel and look into some failures. The most probable strength of a steel beam is given by 24Y^(-0.05) kips where Y is the number of cycles. This value is known to 25% with 90% confidence.

a) How many cycles will elapse before the beam loses 20% of its strength?

b) Suppose the cyclic load on the beam is 10 kips. How many cycles will occur before the probability of failure reaches 10%. Assume this can be described by a lognormal distribution.