Apply the concept of Central Limit Theory If random variable

Apply the concept of Central Limit Theory.

If random variables X1, X2, X3, ... Xn follows Uniform(0,10) distribution, the mean (of X1, X2, X3, ... Xn) will be approximately normally distributed. This approximation improves with larger samples.

True or False?

Solution

TRUE.

Actually, the central limit theorem REQUIRES that the sample size is large enough, so that the sample means become more normally distributed. This is true for any underlying distribution, like a uniform distribution in this case.