Constructing Normal Quantile Plots. In Exercises 17–20, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, and then determine whether the data appear to be from a population with a normal distribution.

Earthquake Depths A sample of depths (km) of earthquakes is obtained from Data Set 21 “Earthquakes” in Appendix B: 17.3, 7.0, 7.0, 7.0, 8.1, 6.8.

The sample of depths in kilometer of earthquakes from data set 21 “Earthquakes” in Appendix B.

The given sample data arranged in increasing order is:

6.8, 7.0, 7.0, 7.0, 8.1, 17.3

In the given data, the sample size is 6. Each value is the proportion of $\frac{1}{6}$of the sample.

So, the cumulative left areas can be expressed as

$\frac{1}{2n},\frac{3}{2n},\frac{5}{2n}, \text{and} \text{so} \text{on}$

For the given sample size,$\text{n}=6$ , the cumulative left areas, can be expressed as

$\frac{1}{12},\frac{3}{12},\frac{5}{12},\frac{7}{12},\frac{9}{12}, \text{and} \frac{11}{12}$

The cumulative left areas expressed in decimal form are 0.0833, 0.2500, 0.4167, 0.5833, 0.75, and 0.9167.

Referring to the standard normal distribution table, the z-score values corresponding to cumulative left areas of 0.0833, 0.2500, 0.4167, 0.5833, 0.75, and 0.9167 are -1.38, -0.67, -0.21, 0.21, 0.67, 1.38.

Pair thesample values of depths of eqarthquakes with the corresponding z-score in the form of (x, y) as:

(6.8,-1.28), (7.0, -0.67), (7.0, -0.21), (7.0, 0.21), (8.1, 0.67), and (17.3,1.38)

Steps to draw a Normal quantile plot are as follows:

1. Make horizontal axis and vertical axis.
2. Mark the points 6, 8, 10 up to 18 on the horizontal axis and points -1.5, -1.0, - 0.5, 0.00 up to 1.5.
3. Provide a title to the horizontal and vertical axis as “X values” and “Z-score” respectively.
4. Mark the co-ordinates and obtain the normal quantile plot as shown below.

From the normal quantile plot, the points are not linearly aligned and do not show any symmetric pattern. So, the sample depths of earthquakes do not appear to be from a normal distributed population.