6.126 The grains comprising polycrystalline metals tend to have weights that follow a lognormal diss tribution. For a certain type of aluminum, gram weights have a lognormal distribution with and (in units of 10–2 gram).
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 Tchebysheff’s theorem.]
c Find the probability that a randomly chosen grain weighs less than the mean gram weight.