In a particular country, 35 per cent of the population is estimated to have at least one mobile phone.
A sample of 40 people is selected from the population.
Use the distribution \(\mathrm { B } ( 40,0.35 )\) to estimate the probability that the number of people in the sample that have at least one mobile phone is:
at most 15 ;
more than 10 ;
more than 12 but fewer than 18 ;
exactly equal to the mean of the distribution.
In the same country, 70 per cent of households have a landline telephone connection.
A sample of 50 households is selected from all households in the country.
Stating a necessary condition regarding this selection, estimate the probability that fewer than 30 households have a landline telephone connection. [0pt]
[4 marks]