No, just do what the question tells you to. If it asks for smaller than 9, do <9, not <= 8. You can do continuity correction if you want but it seems it’s not necessary for hsc.
As a straight binomial probability,
![](https://latex.codecogs.com/png.latex?\bg_white P(X < 9))
and
![](https://latex.codecogs.com/png.latex?\bg_white P(X \le 8))
are the same thing because
![](https://latex.codecogs.com/png.latex?\bg_white X \in \{0,\,1,\,2,\,...\,n\})
.
In taking a normal approximation, a discrete distribution is approximated by a continuous one, which is why the continuity correction is needed.
Suppose you toss a fair coin 10,000 times. The most likely outcome is 5,000 heads, with probability
You have no hope of finding a value like 10,000! with a calculator, and the approximation I've used here (using Stirling's formula for
n!) would need to be given in a question.
It can be estimated easily with a normal distribution, however, but only if a continuity correction is applued. Without it:
but, after applying the appropriate correction,
the probability can be found from a
z-score table.