Expected value of Sampling Distribution

Consider the following population of ten scores: 4,4,4,5,5,6,6,8,9,9.

What is the expected value of the sampling distribution of the mean for n =3, when drawing from this population of scores? What is the Standard Error?

My thoughts:

Regardless of the shape of the population from which we are sampling, the sampling distribution of the sample mean will have a mean μ equal to the mean of the population from which we are sampling, and a standard deviation equal to σ/ sqrt(n) which equals the standard error (SE).

Therefore μ = (4*3+5*2+6*2+8+9*2)/10 = 6 and then σ = 1.89737, n=3 => SE = 1.09545


Any help is appreciated