(i) Let the random variable \(X\) represent the number of days with more than 20 cm of snow in a 7-day period. \(X\) follows a binomial distribution with parameters \(n = 7\) and \(p = 0.21\).

We need to find \(P(X < 5)\), which is \(1 - P(X \geq 5)\).

Calculate \(P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)\).

\(P(X = 5) = \binom{7}{5} (0.21)^5 (0.79)^2\)

\(P(X = 6) = \binom{7}{6} (0.21)^6 (0.79)^1\)

\(P(X = 7) = \binom{7}{7} (0.21)^7\)

\(P(X \geq 5) = 21(0.21)^5(0.79)^2 + 7(0.21)^6(0.79) + (0.21)^7\)

\(P(X \geq 5) = 0.006 + 0.0003 + 0.0000008 \approx 0.0063\)

Thus, \(P(X < 5) = 1 - 0.0063 = 0.994\).

(ii) Let \(Y\) be the number of 7-day periods with at least 1 day of more than 20 cm of snow. The probability of at least 1 day with more than 20 cm of snow in a 7-day period is \(1 - (0.79)^7 = 0.808\).

\(Y\) follows a binomial distribution with parameters \(n = 4\) and \(p = 0.808\).

We need to find \(P(Y = 3)\).

\(P(Y = 3) = \binom{4}{3} (0.808)^3 (0.192)^1\)

\(P(Y = 3) = 4(0.808)^3(0.192)\)

\(P(Y = 3) = 4(0.527)(0.192) \approx 0.405\).