Question

The following table displays finishing times, in seconds for the winners of fourteen 1-mile thoroughbred horse race, as found in Thoroughbred Times.

Part (a): Use Table III in Appendix A to construct a normal probability plot of the given data.

Part (b): Use part (a) to identify any outliers.

Part (c): Use part (a) to access the normality of the variable under consideration.

Short answer

Part (a): The required normal probability plot is given below,

Part (b): There are no outliers for the given data.

Part (c): The finishing time is approximately normally disturbed.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given question,

Part (a) Step 2. Construct a normal probability plot.

The variable is finishing time. To construct a normal probability plot, we first arrange the data in increasing order and obtain the normal scores from normal scores table.

The ordered data are shown in the first column of the below table; the normal scores form $n=14$column of normal scores table, are shown in the second column of the below table.

Part (a) Step 3. Plot the points.

Plot the points using horizontal axis for the final exam scores and the vertical axis for the normal scores,

Part (b) Step 1. Identify any outliers.

Consider the normal probability plot from part (a),

We can observe that no observations fall outside the overall pattern of the data.

So, there are no outliers in the data.

Part (c) Step 1. Access the normality of the variable under consideration.

Consider the normal probability plot from part (a),

The above normal probability plot is roughly linear. So, we can assume that the finishing time is approximately normally disturbed.