Suppose that computations are only carried out with k decimal digits. The other digits are rounded up to the nearest valule. For example if k= 2 the number 0.7751 will be rounded as 0.78 but 0.7730 will be rounded as 0.77. The error of a computation is defined as the difference of the exact value minus the rounded value. By using the Central Limit Theorem compute the probability that the error of adding n numbers will be less than 1/100 in absolute value. When n = 100 and k = 3 the closest value to this probability is: (A) 75% (B) 84% (C) 99% (D) 99.9% (E) 75.9%

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Suppose that computations are only carried out with k decimal digits. The other digits are
rounded up to the nearest valule. For example if k = 2 the number 0.7751 will be rounded as
0.78 but 0.7730 will be rounded as 0.77. The error of a computation is defined as the difference
of the exact value minus the rounded value. By using the Central Limit Theorem compute the
probability that the error of adding n numbers will be less than 1/100 in absolute value. When
n = 100 and k = 3 the closest value to this probability is:
(A) 75%
(B) 84%
(C) 99%
(D) 99.9%
(E) 75.9%
Transcribed Image Text:Suppose that computations are only carried out with k decimal digits. The other digits are rounded up to the nearest valule. For example if k = 2 the number 0.7751 will be rounded as 0.78 but 0.7730 will be rounded as 0.77. The error of a computation is defined as the difference of the exact value minus the rounded value. By using the Central Limit Theorem compute the probability that the error of adding n numbers will be less than 1/100 in absolute value. When n = 100 and k = 3 the closest value to this probability is: (A) 75% (B) 84% (C) 99% (D) 99.9% (E) 75.9%
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