(i)[4]
In one country, $68\%$ of households own a printer. Determine the probability that, from a random sample of $8$ households, exactly $5$, $6$ or $7$ of them have a printer.
(ii)[5]
Use an approximation to determine the probability that, in a random sample of $500$ households, more than $337$ households own a printer.
(iii)[1]
Explain why the approximation in part (ii) is justified.