7 In the region of Arka, the total number of households in the three villages Reeta, Shan and Teber is 800 . Each of the households was asked about the quality of their broadband service. Their responses are summarised in the following table.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Quality of broadband service |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Excellent | Good | Poor |
| \multirow{3}{*}{Village} | Reeta | 75 | 118 | 32 |
| \cline { 2 - 5 } | Shan | 223 | 177 | 40 |
| \cline { 2 - 5 } | Teber | 12 | 60 | 63 |
- Find the probability that a randomly chosen household is in Shan and has poor broadband service.
- Find the probability that a randomly chosen household has good broadband service given that the household is in Shan.
In the whole of Arka there are a large number of households. A survey showed that \(35 \%\) of households in Arka have no broadband service.
- 10 households in Arka are chosen at random.
Find the probability that fewer than 3 of these households have no broadband service.
- 120 households in Arka are chosen at random.
Use an approximation to find the probability that more than 32 of these households have no broadband service.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.