Math Solutions

Solution: Forty-eight measurements are recorded to several decimal places. Each of the 48 numbers is rounded off to the nearest integer. The sum of the

Question: Forty-eight measurements are recorded to several decimal places. Each of the 48 numbers is rounded off to the nearest integer. The sum of the original 48 numbers is approximated by the sum of these integers. If we assume that the errors made by rounding off are stochastically independent and have a uniform distribution over the interval \((-0.5,0.5)\), compute the approximate probability that the sum of the integers is within 2 units of the true sum. (Hint: Central limit theorem (again!) and the standard normal tables)

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