In preparing next quarter's budget, the accountant for a small business has one hundred different expenditures to account for. Her predecessor listed each entry to the penny, but doing so grossly overstates the precision of the process. A more truthful alternative, she intends to record each budget allocation to the nearest $ 100. What is the probability that the total estimated budget will end up differing from the actual cost by more than $ 500? Assume that Y1, Y2, . . . , Y100, the rounding errors she makes on the one hundred items, are independent and uniformly distributed over the interval [-$ 50, $ 50]. Hint: Consider the total rounding error= S100 = Y1 + Y2 + . . . + Y100.