5 On average, 1 in 2500 adults has a certain medical condition.\\
(i) Use a suitable approximation to find the probability that, in a random sample of 4000 people, more than 3 have this condition.\\
(ii) In a random sample of $n$ people, where $n$ is large, the probability that none has the condition is less than 0.05 . Find the smallest possible value of $n$.

\hfill \mbox{\textit{CAIE S2 2015 Q5}}