verifying the assumption of a normal distribution 

How do you verify that the assumption of a normal distribution is correct  if you have only the mean and standard deviation? What could you do if you actually have the data? In my case, the sample size is 1000, mean 40, and SD 10. 

If you have only the mean and standard deviation, then it is impossible to test if the assumption of a normal distribution is correct .

If you have data, then you can use chi squared test to test it.

**************WE'RE DOING BASIC STATS, HAVEN'T DONE CHI-SQUARED YET. IS THERE A MORE BASIC WAY? MAKE A HISTOGRAM?*************

If you then took a sample of 20 from the original sample of 1000, is the expected value 40? How do you find the standard deviation for the sample of 20?

Suppose that the sample size is 1000, mean 40, and SD 10, and If you then took a sample of 20 from the original sample of 1000(NOW, the original sample is the population).

This is a question, you know the distribution of population is normal distribution, what is the sample distribution.

We know that if the distribution of population is normal distribution with mean , then the distribution of a sample with size n=20 is also a normal distribution with mean  and standard deviation is
                           
So, the standard deviation for the sample of 20 is 2.236, and the mean is 40.

*****************AS THIS SAMPLE OF 20 IS FROM A FINITE POPULATION OF 1000, WHY DON'T YOU USE :

SQUARE ROOT OF N-n/N-1 * STDEV/ SQUARE ROOT OF n   ? ****************