A system consists of components A and B connected in series, as shown in the following schematic illustration. The lifetime in months of component A is lognormally distributed with μ = 1 and σ = 0.5, and the lifetime in months of component B is lognormally distributed with μ = 2 and σ = 1. The system will function only so long as A and B both function.

a. Generate, by simulation, a large number (at least 1000) of system lifetimes.
b. Estimate the mean system lifetime.
c. Estimate the probability that the system fails within 2 months.
d. Estimate the 20th percentile of system lifetimes.
e. Construct a normal probability plot of system lifetimes. Is the system lifetime approximately normally distributed?
f. Construct a histogram of the system lifetimes. Is it skewed to the left, skewed to the right, or approximately symmetric?

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A B