Ray is a bit off track, there are indeed a few mathematicians around Fixya.
Here you are dealing with the standard error of a proportion. The proportion of students of interest in the sample is 540/970 = 0.5567. This is usually denoted by p.
Now you want the standard error of this proportion, s. It is
SQRT ( p (1-p) / N ) where N is sample size. Note the error is smaller for big samples. Here s = 0.0160.
Now we turn to the Normal Distribution. We want the Z-statistic which corresponds to a confidence level of 92%, or 0.92. Z is the number of Standard Deviations on the Normal Curve which takes in 92% of the area under the curve. You can look this up in any table of the Normal Distribution, or with an online calculator
This gives Z = 1.751. So the true result is somewhere in p ± (1.751 * 0.0160)
or 0.5567 ± 0.0279. The margin of error is 0.0279.
Now I don't know here if your tutor wants you to use a Continuity Correction, which is sometimes applied because we are approximating the Normal Distribution here. If so this is
0.5 / N = 0.5 / 970 = 0.0005.
This small amount is added to the Margin of Error, to make 0.0284.
A good reference for you to use is