In real life computation, we can only round irrational numbers to certain number of decimal places, such as pi =  3.141592654 and e = 2.718281828. If we round the numbers to five decimal places, we have π' = 3.14159 and e'  = 2.71828. For any real number x, we round it up/down to five decimal places, denoted by x', so the error e = x - x' is induced. Assume we have 10000 x's  in five de

In real life computation, we can only round irrational numbers to certain number of decimal places, such as pi =  3.141592654 and e = 2.718281828. If we round the numbers to five decimal places, we have π' = 3.14159 and e'  = 2.71828. For any real number x, we round it up/down to five decimal places, denoted by x', so the error e = x - x' is induced.

Assume we have 10000 x's  in five decimal places, use CLT to determine the integer k, such that we are 99.74% sure that the absolute value of the sum of 10000 errors is less than  k x standard deviation of the sum of 10000 errors(Round your result up/down in 7 decimal places during calculation)