I am working on the following question but I'm not sure if my approach is correct.
Given that X~U(4,8), I need to find the distribution of the sample mean for a sample size 30.
My approach is that calculate the mean and standard deviation of X first, which are 6 and 1.1547 respectively. Then, the standard deviation of the sample mean will be 1.1547/sqrt(30) = 0.2108.
Since the sample size is greater or equal to 30, the distribution of the sample mean will follow a normal distribution, that is N(0.2, 0.2108).
Can someone help me to correct it if I am wrong.
