An article in Chemosphere [“Statistical Evaluations Reflecting the Skewness in the Distribution of TCDD Levels in Human Adipose Tissue” (1987, Vol.16(8), pp. 2135- 2140)] concluded that the levels of 2,3,7,8-TCDD (colorless persistent environmental contaminants with no distinguishable odor at room temperature) in human adipose tissue has a lognormal distribution (based on empirical evidence from North America). The mean and variance of this lognormal distribution in the USA are 8 and 21, respectively. Let X denote this lognormal random variable. Determine the following:

(a) P(2000 < X < 2500)

(b) Value exceeded with probability 10%

(c) Mean and variance of X