7. A randomly selected real number A is rounded off to its nearest integer RA. It is reasonable to assume that the round-off error A − RA is uniformly distributed in (−0.5, 0.5). If 52 numbers are rounded off to the nearest integer and then averaged, approximate the probability that the absolute value of the average error of the 52 numbers is more than 0.1.
Answers
Given : A randomly selected real number A is rounded off to its nearest integer RA. It is reasonable to assume that the round-off error A − RA is uniformly distributed in (−0.5, 0.5).
52 numbers are rounded off to the nearest integer and then averaged, approximate
To Find : the probability that the absolute value of the average error of the 52 numbers is more than 0.1.
Solution:
uniformly distributed in (−0.5, 0.5).
Approx SD = (0.5 -(-0.5))/6 = 1/6
SE = SD/√n SE = Standard Error
=> SE = (1/6)/√52
=> SE = 0.0231
absolute value of the average error of the 52 numbers is more than 0.1
Hence not between -0.1 and 0.1
Mean = 0
z score = ± ( 0.1 - 0)/0.0231 = ±4.326
Hence almost 100 % Data lies between -0.1 and 0.1
Hence almost there is no probability that the absolute value of the average error of the 52 numbers is more than 0.1.
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