Consider if we are simply given that 
latex \mathrm{P}(X < 4.2) = 0.2
latex \mathrm{P}(X > 8) = 0.1
latex \alpha \mathrm{P}(X < \mu_0 – \alpha) = \mathrm{P}(X < \mu_0 + \alpha)![. In this case we cannot really doing our usual approach of doing standardising and inverse normal since we lack the area. [caption id="attachment_1656" align="alignnone" width="1280"]<a href="http://theculture.sg/wp-content/uploads/2015/09/Normal-Distribution-Curve.png"><img class="wp-image-1656 size-full" src="http://theculture.sg/wp-content/uploads/2015/09/Normal-Distribution-Curve.png" alt="Normal Distribution Curve" width="1280" height="587" /></a> Normal Distribution Curve[/caption] Considering the symmetrical properties of the graph above, we can derive some results. Many students tend to confuse and think that normal distribution is always centred about zero, this is inaccurate as only the standard normal distribution is centred about zero. In general, we can say that normal distribution is always centred about its mean,](http://theculture.sg/wp-content/ql-cache/quicklatex.com-9c9daa331cea5595f327332bad31e07c_l3.png "Rendered by QuickLaTeX.com")
latex \mu$. And it so happens that the mean of the standard normal distribution is zero.
Students may want to reference a 2014 ACJC Prelim Question here to see if they can do it.
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