Repeated sample of 36 are drawn from a population with mean 52 and standard deviation 18. What is the standard deviation of the distribution of the sample means?
To find the standard deviation of the distribution of the sample means, you need to calculate the standard deviation, also known as the standard error, of the sample means. This can be done by using the formula:
Standard deviation of the sample means = (Standard deviation of the population) / √(sample size)
In this case, the standard deviation of the population is given as 18, and the sample size is 36.
Plugging these values into the formula, we get:
Standard deviation of the sample means = 18 / √(36)
Simplifying the expression, we have:
Standard deviation of the sample means = 18 / 6
Calculating the division gives us:
Standard deviation of the sample means = 3
Therefore, the standard deviation of the distribution of the sample means is 3.