Another problem on Estimation

Please help me to solve the following problem.

A computer in adding numbers, rounds each number to the nearest integer. All the rounding errors are independent and come from a uniform distribution over the range [-0.5,0.5].
Find how many numbers can be added together so that the probability that the magnitude of the total error is less than 10 is at least 0.95.

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Originally Posted by Sashikala

Please help me to solve the following problem.

A computer in adding numbers, rounds each number to the nearest integer. All the rounding errors are independent and come from a uniform distribution over the range [-0.5,0.5].
Find how many numbers can be added together so that the probability that the magnitude of the total error is less than 10 is at least 0.95.

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Hi Sashikala,

Let's say you have n numbers and the sum of the rounding errors is X. A Uniform[-0.5, 0.5] distribution has a mean of 0 and a variance of 1/12; so the mean of X is 0 and its variance is n/12.

I think we can safely assume by the Central Limit Theorem that X has an approximately Normal distribution. So you want to find n such that

.

You know the mean and variance of X, so ....

I get it.
So the rest have to be done as follows
P(-10/RT(n/12) < Z < 10/RT(n/12) >=0.95
ie -1.96 < Z < 1.96
so 10/RT(n/12) = 1.96
n=312

Thanks very much.