Lan starts a new job on Monday. He will catch the bus to work every day from Monday to Friday inclusive. The probability that he will get a seat on the bus has the constant value \(p\). The random variable \(X\) denotes the number of days that Lan will catch the bus until he is able to get a seat. The probability that Lan will not get a seat on the Monday, Tuesday, Wednesday or Thursday of his first week is 0.4096 .
(i) Show that \(p=0.2\).

(ii) Find the probability that Lan first gets a seat on Monday of the second week in his new job.

(iii) Find the least integer \(N\) such that \(\mathrm{P}(X \leqslant N)>0.9\), and identify the day and the week that corresponds to this value of \(N\).