N2015 P2 Q7

The average number of errors per page for a certain daily newspaper is being investigated.

1. State, in context, two assumptions that need to be made for the number of errors per page to be well modelled by a Poisson distribution.[2]

Assume that the number of errors per page has the distribution \(\mathrm{Po}(1.3)\).

2. Find the probability that, on one day, there are more than \(10\) errors altogether on the first \(6\) pages.[3]
3. The probability that there are fewer than \(2\) errors altogether on the first \(n\) pages of the newspaper is less than \(0.05\). Write down an inequality in terms of \(n\) to represent this information, and hence find the least possible value of \(n\).[2]