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                    When
one batch of a certain chemical product is prepared the amount of a
certain impurity (which we will call x) in it is
a random variable
                    with
a mean of X_bar = 4.0 grams and a standard
deviation of s_x = 2.9 grams. If 180 independent
batches of the chemical are produced what is the (approximate)
probability of the
                    average
amount of the impurity per batch in the 180-batch sample being more
that 4.6 grams? (Hint: if the average amount of
                    impurity
per batch were more than 4.6
grams, then the 180 batch sample would contain a total
                    of
more than 828 g of the impurity.)