- A research project into food purchases found that \(35 \%\) of people who buy eggs do not buy free range eggs.
A random sample of 30 people who bought eggs is taken. The random variable \(F\) denotes the number of people who do not buy free range eggs.
- Find \(\mathrm { P } ( F \geqslant 12 )\)
- Find \(\mathrm { P } ( 8 \leqslant F < 15 )\)
A farm shop gives 3 loyalty points with every purchase of free range eggs. With every purchase of eggs that are not free range the farm shop gives 1 loyalty point. A random sample of 30 customers who buy eggs from the farm shop is taken.
- Find the probability that the total number of points given to these customers is less than 70
The manager of the farm shop believes that the proportion of customers who buy eggs but do not buy free range eggs is more than \(35 \%\)
In a survey of 200 customers who buy eggs, 86 do not buy free range eggs.
Using a suitable test and a normal approximation,
- determine, at the \(5 \%\) level of significance, whether there is evidence to support the manager's belief. State your hypotheses clearly.