The sampling distribution of x bar must be a normal distribution with a mean 0 and standard deviation 1. true or false
Although I'm not sure what you mean by "x bar," is it a sample mean?
If so, it is false.
False. The sampling distribution of x bar is not always a normal distribution with a mean of 0 and standard deviation of 1.
The sampling distribution of x bar follows a normal distribution when the sample size is large enough and the population distribution is approximately normal. In this case, the mean of the sampling distribution is equal to the population mean and the standard deviation is equal to the population standard deviation divided by the square root of the sample size.
If the population distribution is not approximately normal, the sampling distribution of x bar may still be approximately normal due to the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of x bar approaches a normal distribution regardless of the shape of the population distribution.
Therefore, the statement that the sampling distribution of x bar must have a mean of 0 and standard deviation of 1 is incorrect. The mean and standard deviation of the sampling distribution depend on the characteristics of the population distribution and the sample size.