An unknown distribution has a mean of 90 and a standard deviation of 16. Samples of size n=64 are drawn randomly from the population. What is the standard deviation of sample mean?
The standard deviation of the sample mean (also known as the standard error) can be calculated using the formula:
Standard deviation of sample mean = Standard deviation / √(sample size)
In this case, the standard deviation of the population is given as 16 and the sample size is 64. So, we can substitute these values into the formula:
Standard deviation of sample mean = 16 / √(64)
Taking the square root of 64 gives us:
Standard deviation of sample mean = 16 / 8
Simplifying further, we have:
Standard deviation of sample mean = 2
Therefore, the standard deviation of the sample mean is 2.