8 At a wine-tasting competition, two judges give marks out of 100 to 7 wines as follows.
| Wine | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| Judge I | 86.3 | 87.5 | 87.6 | 88.8 | 89.4 | 89.9 | 90.5 |
| Judge II | 85.3 | 88.1 | 82.7 | 87.7 | 89.0 | 89.4 | 91.5 |
- A spectator claims that there is a high level of agreement between the rank orders of the marks given by the two judges. Test the spectator's claim at the \(1 \%\) significance level.
- A competitor ranks the wines in a random order. The value of Spearman's rank correlation coefficient between the competitor and Judge I is \(r _ { s }\).
(a) Find the probability that \(r _ { s } = 1\).
(b) Show that \(r _ { s }\) cannot take the value \(\frac { 55 } { 56 }\).