= Solution
Sort the observations into <order statistics> $x_{(1)}\leq\cdots\leq x_{(n)}$. Choose <plotting positions> $p_i=(i-1/2)/n$ and calculate the <standard normal quantiles> $z_i=\Phi^{-1}(p_i)$. The <normal Q-Q plot> consists of the pairs $(z_i,x_{(i)})$.
If the <normal distribution> model is appropriate, the points should lie approximately on a straight line with positive slope, because its population <quantile function> is
$$
Q(p)=\mu+\sigma\Phi^{-1}(p).
$$
The intercept is approximately $\mu$ and the slope approximately $\sigma$; neither needs to be known in advance. The reference need not be the identity line. One justification is the <probability integral transform>: for an independent normal <statistical sample>, $\Phi((X_{(i)}-\mu)/\sigma)$ are uniform <order statistics>, whose typical values are near their <plotting positions>. The equality is approximate for a finite sample, particularly at the extremes. Systematic curvature, unusually heavy tails, or isolated extreme departures argue against the proposed distributional shape. A straight marginal <Q-Q plot> does not itself establish <independence> of observations.
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