Question

assume that x does not follow a normal distribution, and we take samples of size 16. can you apply the clt to conclude that \\(\bar{x}\\) follows a normal distribution?
yes
no
question 4
1 pts
additional question:
assume that x does not follow a normal distribution, and we take samples of size 45. can you apply the clt to conclude that \\(\bar{x}\\) follows a normal distribution?
yes
no

Explanation:

The Central Limit Theorem (CLT) states that for a sample size \(n\), if \(n\) is large (usually \(n\geq30\)), the sampling distribution of the sample mean \(\bar{X}\) is approximately normal, regardless of the distribution of the population from which the sample is drawn. In the first case, \(n = 16<30\), so we cannot apply the CLT. In the second case, \(n = 45\geq30\), so we can apply the CLT.

Answer:

For the first question: No.
For the second question: Yes.