(i) To find the standard deviation \(\sigma\), we use the z-score formula:

\(z = \frac{X - \mu}{\sigma}\)

Given \(X = 73\), \(\mu = 75\), and \(z = -1.036\) (from the z-table for 15%), we have:

\(-1.036 = \frac{73 - 75}{\sigma}\)

Solving for \(\sigma\):

\(\sigma = \frac{2}{1.036} \approx 1.93\)

(ii) The probability that a roll is longer than 77 m is 0.15. We need to find the probability that fewer than 3 out of 8 rolls are longer than 77 m. This is a binomial probability problem with \(n = 8\) and \(p = 0.15\).

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

\(= (0.85)^8 + \binom{8}{1}(0.15)(0.85)^7 + \binom{8}{2}(0.15)^2(0.85)^6\)

\(= 0.895\)