If Y has a log-normal distribution with parameters and 2, it can be shown that E(Y ) =
Chapter 4, Problem 4.183(choose chapter or problem)
If Y has a log-normal distribution with parameters and 2, it can be shown that E(Y ) = e(+2)/2 and V(Y ) = e2+2 (e2 1). The grains composing polycrystalline metals tend to have weights that follow a log-normal distribution. For a type of aluminum, gram weights have a log-normal distribution with = 3 and = 4 (in units of 102 g). a Find the mean and variance of the grain weights. b Find an interval in which at least 75% of the grain weights should lie. [Hint: Use Tchebysheffs theorem.] c Find the probability that a randomly chosen grain weighs less than the mean grain weight.
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