An unknown population X has a mean of 128 and a standard deviation of 32. A random sample of size n=64 are drawn from the population.

Is the sampling distribution normal? Why?

Yes, the sampling distribution is expected to be normal. This is because, according to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution regardless of the shape of the population distribution. In this case, the population mean (128) and standard deviation (32) are known, and since the sample size is reasonably large (n=64), we can expect the sampling distribution to be approximately normal.