The grains composing polycrystalline metals tend to have weights that follow a log-normal distribution. For a certain type of aluminum, gram weights, X can be modeled by a lognormal distribution with = 3 and = 4 (in the units of 10-2 gram). a. Find the mean of the grain weights. b. Find the variance of the grain weights. c. Find the interval in which at least 75% of the grain weights should lie. d. Find the probability that a randomly chosen grain weighs less than the mean grain weight. e. Find the median value of grain weight. f. If five different samples of grain of this type are randomly selected, what is the probability that at least 2 will weigh less than the mean weight?