Answer the question:

A certain factory produces Xn specialized parts on day n, where Xn are independent and identically distributed random variables with mean 6 and variance 9. Let Sn be the total number of specialized parts produced from day 1 to day n. using central limit theorem, determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.c. determine the maximum value of a so that " ( Sgo = a) 2 0.999 . Note: This maximum value must be a whole number