When a pesticide comes into contact with skin, a certain percentage of it is abs

Question

When a pesticide comes into contact with skin, a certain percentage of it is absorbed. The percentage of the pesticide that will be absorbed during a given tie period can be modeled with a lognormal distribution. Assume that for a given pesticide, the amount that is absorbed (in percent) in a two-hour time peroid is log normally distributed with mu=1.5 and sigma=0.5.

1. Find the mean percentage absorbed.
2. Find the median percentage absorbed.
3. Find the probability that the percent absorbed is more than 10.
4. Find the probability that the percent absorbed is less than 5.
5. During the two hour period, an intermediate reading reveals that the percent absorbed is 3 percent. What is the probability that the amound absorbed at the end of the two hour period will be greater than 5 percent?

Explanation / Answer

1) For lognormal
mean = e^(mu + sigma^2/2)= e^(1.5+0.5^2/2)=5.078

2) median = e^mu = e^1.5 = 4.48

3) P(x>10)= 1- P(x<10)

P(x<10) = 1/2 erfc( (mu - log(x))/(sqrt(2)*sigma))

=1/2 erfc( (1.5 - log(10))/(sqrt(2)*.5))=0.946

so P(x>10) =1-0.946 = .054 = 5.4 %

4) P(x<5) = 1/2 erfc( (1.5 - log(5))/(sqrt(2)*.5))=.587=58.7 %

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