- In a local council, \(60 \%\) of households recycle at least half of their waste. A random sample of 80 households is taken.
The random variable \(X\) represents the number of households in the sample that recycle at least half of their waste.
- Using a suitable approximation, find the smallest number of households, \(n\), such that
$$\mathrm { P } ( X \geqslant n ) < 0.05$$
The number of bags recycled per family per week was known to follow a Poisson distribution with mean 1.5
Following a recycling campaign, the council believes the mean number of bags recycled per family per week has increased. To test this belief, 6 families are selected at random and the total number of bags they recycle the following week is recorded.
The council wishes to test, at the 5\% level of significance, whether or not there is evidence that the mean number of bags recycled per family per week has increased.
- Find the critical region for the total number of bags recycled by the 6 families.