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However , in the following question , i don't know how to identify whether the standard deviation given is standard deviation of sample or standard deviation of population ... Can anyone help me to idenitify it ?

At a large university , the mean age of students is 22.3 years and the standard deviation is 4 years . A random sample of 64 students is drawn . What is the probability that the average of these students is greater than 23 years ?

Based on the author , the 4 given is standard deviation of population .

Th standard deviation of mean is 4 / sqrt(64) ..

Why is it so ?

I think it's wrong because we only picked 64 students out of the population , so the standard deviation we get is the standard deviation of sample , not the standard deviation of population