A manufacturer of sweets knows that \(8 \%\) of the bags of sugar delivered from supplier \(A\) will be damp.
A random sample of 35 bags of sugar is taken from supplier \(A\).
Using a suitable model, find the probability that the number of bags of sugar that are damp is
exactly 2
more than 3
Supplier \(B\) claims that when it supplies bags of sugar, the proportion of bags that are damp is less than \(8 \%\)
The manufacturer takes a random sample of 70 bags of sugar from supplier \(B\) and finds that only 2 of the bags are damp.
Carry out a suitable test to assess supplier B's claim.
You should state your hypotheses clearly and use a \(10 \%\) level of significance.