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.

McDonald’s Dinner Service Times A sample of drive-through service times (seconds) at McDonald’s during dinner hours, as listed in Data Set 25 “Fast Food” in Appendix B: 84, 121, 119, 146, 266, 181, 123, 152, 162.

The sample of drive through service times in seconds at McDonalds during dinner hours from data set 25 “Fast Food” in Appendix B.

The given sample data in increasing order is:

84, 119, 121, 123, 146, 152, 162, 181, 266.

In the given data, the sample size is 9. Each value is the proportion of $\frac{1}{9}$of the sample.

So, the cumulative left areas, can be expressed in general as $\frac{1}{2n},\frac{3}{2n},\frac{5}{2n}, \text{and} \text{so} \text{on}$.

For the given sample size,$\text{n}=8$ , the cumulative left areas, can be expressed as

$\frac{1}{18},\frac{3}{18},\frac{5}{18},\frac{7}{18},\frac{9}{18},\frac{11}{18},\frac{13}{18},\frac{15}{18} \text{and} \frac{17}{18}$

The cumulative left areas expressed in decimal form are 0.0555, 0.1667, 0.2778, 0.3889, 0.5000, 0.6111, 0.7222, 0.8333, and 0.9444.

Refer to the standard normal distribution table, the z-score values corresponding to 0.0555, 0.1667, 0.2778, 0.3889, 0.5000, 0.6111, 0.7222, 0.8333, and 0.9444 for left-tailed areas is equal to -1.59, -0.97, -0.59, -0.28, 0.00, 0.28, 0.59, 0.97, 1.59.

Pair thesample values ofdrive-through service times at McDonald’s during dinner hours with the corresponding z-score in the form of (x, y) as:

(84,-1.59), (119, -0.97), (121, -0.59), (123, -0.28), (146, 0), (152, 0.28), (162, 0.59), (181, 0.97), (266, 1.59)

Steps to draw Normal quantile plot are as follows:

1. Make horizontal axis and vertical axis.
2. Mark the points 80, 100, 120 up to 280 on the horizontal axis and points -1.5, -1.0, -0.5, up to 1.
3. Provide title to horizontal and vertical axis as “X values” and “Z-score” respectively.
4. Mark the coordinates on the plot and obtain the normality plot as shown below.

From the normal quantile plot, the point shows a symmetric pattern close to linearity. So, the sample of drive through service time at McDonalds during dinner hours appears to be from a normally distributed population.