The central limit theorem states that the sampling distribution of a sample mean is approximately normal if the sample size is large enough, even if the population distribution is not normal. The central limit theorem also states that the sampling distribution will have the following properties:
1. The mean of the sampling distribution will be equal to the mean of population distribution:
x = μ
2. The standard deviation of the sampling distribution will be equal to the standard deviation of the population distribution divided by the sample size:
s = σ / √n
To find the sample mean and sample standard deviation of a given sample, simply enter the necessary values below and then click the “Calculate” button.
Sample mean (x) = 17
Sample standard deviation (s) = 0.8