We have the population of 3000 students. The average height of this population is 180 cm with the standard deviation of 5 cm. We pick 25 random students and measure their height.

What is the expected value and standard deviation for the average height of this sample?

I was thinking about this, but my conclusion is that the average will be 180cm with 5 cm standard deviation if we pick a sample of 25 students.

I know it's wrong but, can someone explain this with mathematical formulas and philosophical idea behind it.

thank you.