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.
Find the mean and the standard deviation of the sampling distribution of the means
The mean of the sampling distribution of the means is equal to the population mean, which is 128. This is due to the property of sampling distributions, where the mean of the sampling distribution of the means is equal to the population mean.
The standard deviation of the sampling distribution of the means (also known as the standard error of the mean) is given by the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 32 and the sample size is 64.
Standard deviation of the sampling distribution of the means = population standard deviation / sqrt(sample size)
= 32 / sqrt(64)
= 32 / 8
= 4
Therefore, the mean of the sampling distribution of the means is 128 and the standard deviation is 4.