(i)[3]
A random sample of $19$ water pistols is selected. Find the probability that at most $2$ do not work properly.
(ii)[3]
In a random sample of $n$ water pistols, the chance that at least one does not work properly exceeds $0.9$. Determine the least possible value of $n$.
(iii)[5]
A random sample of $1800$ water pistols is taken. Use an approximation to find the probability that at least $152$ do not work properly.
(iv)[1]
Justify the approximation used in part (iii).