(i) We use the binomial distribution where the probability of going to the park on any day is 0.6. We need to find the probability of going to the park more than 5 times in 7 days, i.e., 6 or 7 times.

The probability of going exactly 6 times is given by:

\(\binom{7}{6} (0.6)^6 (0.4)^1 = 7 \times 0.046656 \times 0.4 = 0.1306\)

The probability of going exactly 7 times is given by:

\(\binom{7}{7} (0.6)^7 = 1 \times 0.279936 = 0.02799\)

Thus, the probability of going more than 5 times is:

\(0.1306 + 0.02799 = 0.159\)

(ii) The variance of a binomial distribution is given by \(np(1-p)\).

Here, \(n = 30\) and \(p = 0.6\).

So, the variance is:

\(30 \times 0.6 \times 0.4 = 7.2\)