The article “Assessment of Dermopharmacokinetic Approach in the Bioequivalence Determination of Topical Tretinoin Gel Products” (L. Pershing, J. Nelson, et al., J Am Acad Dermatol 2003:740–751) reports that the amount of a certain antifungal ointment that is absorbed into the skin can be modeled with a lognormal distribution. Assume that the amount (in ng/cm²) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.2 and σ = 2.1.

a. Find the mean amount absorbed.

b. Find the median amount absorbed.

c. Find the probability that the amount absorbed is more than 100 ng/cm².

d. Find the probability that the amount absorbed is less than 50 ng/cm².

e. Find the 80th percentile of the amount absorbed.

f. Find the standard deviation of the amount absorbed.