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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.
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