**Instructions:** Use this Normal Probability Plot maker by entering the sample data below and this statistics calculator will provide step-by-step calculation of the required elements to construct the required probability plot.

#### More About the Normal Probability Plot

A normal probability plot is a plot that is typically used to assess the normality of the distribution to which the passed sample data belongs to.

There are different types of normality plots (P-P, Q-Q and other varieties), but they all operate based on the same idea. The theoretical quantiles of a standard normal distribution are graphed against the observed quantiles. Therefore, if the sample data comes from a normality distributed population, then the normal probability plot should look like a 45^{o} line, with random variations about it. If that is not the case, and the pattern of the normal probability plot departs significantly/systematically from the normal probability plot, then one should suspect that the distribution is not normal.

In this concrete case, the data are ordered in ascending order, and we call such data as \(X_1, X_2, ...., X_i , ...., X_n\). For each \(X_i\) in this sequence of ordered data, we compute the theoretical frequencies \(f_i\), which are approximated using the following formula:

\[ f_i = \frac{i - 0.375}{n + 0.25} \]where \(i\) corresponds to the position in the ordered dataset, and we also compute \(z_i\), is corresponding associated z-score as

\[ z_i = \Phi^{-1}(f_i)\]Then, the normal probability plot is obtained by plotting the ordered X-values (your sample data) on the horizontal axis, and the corresponding \(z_i\) values on your vertical axis.

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