On a production line, bags are filled with cement and weighed as they emerge. It is found that \(20 \%\) of the bags are underweight. In a random sample consisting of \(n\) bags, the variance of the number of underweight bags is found to be \(2 \cdot 4\).
Show that \(n = 15\).
Use cumulative binomial probability tables to find the probability that, in a further random sample of 15 bags, the number that are underweight is
less than 3 ,
at least 5 .
Ten samples of 15 bags each are tested. Find the probability that
all these batches contain less than 5 underweight bags,
the fourth batch tested is the first to contain less than 5 underweight bags.