Question

The paper "The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls" (Lubrication Engineering [1984]: \(153-159\) ) reported the following data on bearing load life (in millions of revolutions); the corresponding normal scores are also given: $$ \begin{array}{cccc} \boldsymbol{x} & \text { Normal Score } & \boldsymbol{x} & \text { Normal Score } \\ \hline 47.1 & -1.867 & 240.0 & 0.062 \\ 68.1 & -1.408 & 240.0 & 0.187 \\ 68.1 & -1.131 & 278.0 & 0.315 \\ 90.8 & -0.921 & 278.0 & 0.448 \\ 103.6 & -0.745 & 289.0 & 0.590 \\ 106.0 & -0.590 & 289.0 & 0.745 \\ 115.0 & -0.448 & 367.0 & 0.921 \\ 126.0 & -0.315 & 385.9 & 1.131 \\ 146.6 & -0.187 & 392.0 & 1.408 \\ 229.0 & -0.062 & 395.0 & 1.867 \\ & & & \\ \hline \end{array} $$ Construct a normal probability plot. Is normality plausible?

Short answer

Based on the constructed plot, if the points fall approximately on a straight line, then normality in the data is plausible. If they deviate substantially from a straight line, then it would suggest that the data are not normally distributed.

Step-by-step solution

Order the data

Arrange the data in ascending order. This is an important step because the order of data is the key to create the normal probability plot.

Compute Normal Scores

The normal score for a data point is the value that it would have if it were normally distributed. This can be calculated using a standard statistic software or table. In this situation, normal scores are already given in the problem statement.

Construct the Normal Probability Plot

Plot the ordered data values (\(x\)) on the x-axis and corresponding normal scores on the y-axis. Remember, each point represents a data value and its corresponding normal score.

Analyze the Plot

If the data are approximately normally distributed, the points plotted on the graph should fall approximately on a straight line when plotted against the normal scores. If the points deviate substantially from a straight line, they are not normally distributed.