Question: 12.5. A computer, in adding numbers, rounds each number off to the nearest inte- ger. Suppose that all rounding errors are independent and uniformly distributed

12.5. A computer, in adding numbers, rounds each number off to the nearest inte- ger. Suppose that all rounding errors are independent and uniformly distributed over (-0.5, 0.5).

(a) If 1500 numbers are added, what is the probability that the magnitude of the total error exceeds 15?

(b) How many numbers may be added together in order that the magnitude of the total error is less than 10, with probability 0.90?

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