# Another problem on Estimation

• Apr 22nd 2009, 10:34 AM
Sashikala
Another problem on Estimation

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.
• Apr 22nd 2009, 02:24 PM
awkward
Quote:

Originally Posted by Sashikala

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.

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

$0.95 \leq \Pr(|X| < 10) = \Pr(-10 < X < 10)$.

You know the mean and variance of X, so ....
• Apr 22nd 2009, 08:12 PM
Sashikala
Another problem on Estimation
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.