The ultimate strains of 15 #5 steel reinforcing bars were measured, yielding the results shown below (data from Allen, 1972):

(a) Plot the data on both the normal and lognormal probability papers. From a visual inspection of the plotted data points, which of the two underlying distributions is a better model to represent the probability distribution of the ultimate strain of reinforcing bars? (b) Perform chi-square tests for both the normal and lognormal distributions at a significance level of 2%, and on the basis of the test results, determine which of the two is a more suitable distribution to model the ultimate strains of steel reinforcing bars.

\begin{tabular}{cc|cc|cc} & Ultimate Strain, & Ultimate Strain, & & Ultimate Strain, \\ Bar # & U (in\%) & Bar # & U (in\%) & Bar # & U (in\%) \\ \hline 1 & 19.4 & 6 & 17.9 & 11 & 16.1 \\ 2 & 16.0 & 7 & 17.8 & 12 & 16.8 \\ 3 & 16.6 & 8 & 18.8 & 13 & 17.0 \\ 4 & 17.3 & 9 & 20.1 & 14 & 18.1 \\ 5 & 18.4 & 10 & 19.1 & 15 & 18.6 \\ \hline \end{tabular} \begin{tabular}{cc|cc|cc} & Ultimate Strain, & Ultimate Strain, & & Ultimate Strain, \\ Bar # & U (in\%) & Bar # & U (in\%) & Bar # & U (in\%) \\ \hline 1 & 19.4 & 6 & 17.9 & 11 & 16.1 \\ 2 & 16.0 & 7 & 17.8 & 12 & 16.8 \\ 3 & 16.6 & 8 & 18.8 & 13 & 17.0 \\ 4 & 17.3 & 9 & 20.1 & 14 & 18.1 \\ 5 & 18.4 & 10 & 19.1 & 15 & 18.6 \\ \hline \end{tabular}