1. ## Standard deviation

I know that the standard deviation of sample = standrad deviation of population divided by sqrt(n) ...

However , in the following question , i dont 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

2. ## Re: Standard deviation

You are told that "the standard deviation is 4 years" before a sample is mentioned so that can't be the standard deviation of the sample! The standard deviation of the sample of 64 students is $\displaystyle \frac{4}{\sqrt{64}}= \frac{4}{8}= \frac{1}{2}$.