Assume that the claim of the manufacturers of alloy B is true, that is, . Find approximate distributions for and in terms of using the central limit theorem. (b) Under the same assumption , find an approximate distribution of the difference in the sample means, . Use the fact that the measurements for the 30 specimens of alloy A are independent of those for the 30 specimens of alloy B. (c) Find the probability that the difference in sample means is 4 or greater under the assumption that . (d) Based on the probability found in (c), do you think these data strongly support that alloy A is superior than alloy B