Symmetrical about the mean question

I had a question like this yesterday but this one is a little different it seems i don't really get these ones...

The masses of 17 year old males in a school are normally distributed with a mean of 70 kg and a standard deviation of 6 kg.

c) Find the range of measurements that is symmetrical about the mean and contains 50% of these students

I don't even know how to start this question.. if someone could just give me some hints to get started...

I thought that the mean is already symmetrical about the mean by 50% in a normal distribution...

the answer in the back of the book is 66.0 kg is less than m is less than 74.0kg