YUP, 166 is correct .The CI for a mean is...

.

Now we want , where B is the bound on your error.

Solving for n we get .

If you plug your constants into this, a lower bound for n is... 165.8944 and you should always round UP here.

And they did a good job by using 2.576 for the z percentile, which you can steal from a t table.