Convert weeks to trials and use a variance restriction

According to the school rules, a student who arrives at school after 0730 hours is considered late.

(i) During the school term, a boy cycles to school on 5 days each week. On any given day, the probability that he arrives after 0730 hours is 0.1. For a period of 4 weeks, calculate the probability that he is late on at least one day but not more than 3 days.2 marks

When the boy has cycled to school for the $n$th time, the probability that he arrived at school late at least once is greater than 0.99. Calculate the least value of $n$.2 marks

(ii) A girl travels to school by bus on 5 days a week. Over a long period of time, the variance of the number of days per week on which she is late is 0.8. Given that $p$ denotes the probability that she arrives late and that $p<0.5$, evaluate $p$.3 marks