Men€™s 400-meter record times are shown in Table 32 for various years.

Let r be the men€™s 400-meter record time (in seconds) at t years since 1900.
a. Construct a scatterplot.
b. Is there a linear association, a nonlinear association, or no association?
c. Compute r. On the basis of the scatterplot and r, determine the strength of the association.
d. Is the association positive, negative, or neither? What does that mean in this situation?
e. The lower the record is, the more innovative runners€™ train- ing programs and nutrition plans must be to shave yet more tenths of seconds off the record. Explain what is surprising about the change in the record time from 1950 to 1999 as com- pared with the change in the record time from 1900 to 1950.

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Table 32 Years versus Men's 400-Meter Run Record Times Record Time Record Time (seconds) Year (seconds) 1900 1916 1928 932 1941 47.8 47.4 47.0 46.2 46.0 1950 1960 1968 1988 1999 458 44.9 43.86 43.29 43.18