A random sample of size 36 is to be selected from a population that has a mean μ = 50 and a standard deviation σ of 10. -

- Find the mean of this sampling distribution.
- Find the standard error of this sampling distribution.

With your limited data, the best estimate of the sample mean is the population mean.

Standard Error of the mean (SEm) = SD/√n

To find the mean of the sampling distribution, we use the fact that the mean of a sampling distribution is equal to the population mean. Given that the population mean is μ = 50, it follows that the mean of the sampling distribution would also be 50.

To find the standard error of the sampling distribution, we need to calculate the standard deviation of the sampling distribution. The standard deviation of a sampling distribution is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation is 10 and the sample size is 36. Plugging these values into the formula, we get:

Standard error = σ/√n
= 10/√36
= 10/6
= 1.67 (rounded to two decimal places)

Therefore, the standard error of this sampling distribution is approximately 1.67 (rounded to two decimal places).