The AJAX Disk Co. manufactures compact disks (CDs) for the music industry. As part of its quality-control program, the diameter of each disk is measured using an electronic measuring device. Letting \(X_{1}\) represent the actual diameter of the disk and \(X_{2}\) represent the measured diameter of the disk,

\(\mathrm{E}\left[\begin{array}{l}X_{1} \\ X_{2}\end{array}ight]=\left[\begin{array}{l}4.6775 \\ 4.6775\end{array}ight]\) and \(\operatorname{Cov}(X)=\left[\begin{array}{ll}.00011 & .00010 \\ .00010 & .00010\end{array}ight]\), where \(x_{1}\) and \(x_{2}\) are measured in inches.

(a) What is the correlation between the actual diameter and the measured diameter of the CDs?

(b) Assume that \(P\left(x_{1} \in[4.655,4.700]ight)=1\). Use a graph to elucidate the degree of linear association between \(X_{1}\) and \(X_{2}\) that is represented by the correlation value you calculated in (a).

(c) Given the characteristics of \(\left(X_{1}, X_{2}ight)\) indicated above, the manager of the quality control-department states that the difference between measured and actual disk diameters is no more than .01 inches with probability \(\geq .90\). Do you agree? Why or why not?