A researcher grows cultures of bacteria. Suppose that fter one day\'s growth, th

Question

A researcher grows cultures of bacteria. Suppose that fter one day's growth, the size of the culture has a lognormal distribution with parameters mu = 2.3 and sigma = 0.2. (a) What is the expected size of the culture after one day? (b) What is the median size of the culture after one day? (c) What is the upper quartile of the size of the culture after one day? (d) What is the probability that the size of the culture after one day is greater than 15? (e) What is the probability that the size of the culture after one day is smaller than 6?

Explanation / Answer

a) Expected size is e^(mu+sigma^2/2)=e^(2.3+0.2^2/2)=10.173

b) Median size is e^mu=2.718^2.3=9.972

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