# Sample size required for bivariate normal distribution

I am new here. Would like to ask a question on the sample size requirement for hypothesis testing following.

If I am drawing samples with 2 non correlated variables (say x,y) from a bivariate normal distribution(assumed) with unknown mean and variance.

I would need to determine the CEP or 50% of the population would fall into X < x and Y < y. How much sample size should I be taking?

What I have thought of:

I have tried to think of it as a binomial distribution problem as well (either sample is in or not in a certain radius r = sqrt(x^2 +y ^2) , and setting probability to be p =0.5 variance as p(1-p). Matching against the table for 50% confidence. I have calculated the sample size required to be ~480.

While examining some literature, I have found sample size for Gaussian distribution to be only around 20-30.

Am I making some wrong assumption? What is the more appropriate way to follow?

• What is the CEP? The sentence in which this acronym appears is ungrammatical, making it difficult to decipher. It also seems to be underdetermined: usually a sample size is found by stipulating an upper threshold for the standard error of a statistic. What is that threshold in this case? – whuber May 22 '14 at 16:26
• Sorry for leaving out the details. CEP - stands for circular error probable or 50% of the population should fall within certain parameters defined. I have defined in a 95% confidence interval and 3% margin of error for my attempt to solve this problem – user1538798 May 26 '14 at 3:23
• Well, since we extend the Gaussian to two dimensions essentially, a required sample size of 20^2 = 400 can intuitively makes sense. But I got to this page having the same question you did, so I'm not sure either. – Charlie Jan 30 at 19:18