2024 VJC H1 Q10

In a large retail company, the probability of a telesales representative making a sale on a customer call is constant at \(0.15\) for every call made.

1. Find the probability that, in \(25\) random calls, at least \(7\) but fewer than \(13\) sales are made.[2]
2. If the probability that, in \(100\) random calls, more than \(r\) sales were made is less than \(0.5\), find the least value of \(r\).[3]

Telesales representatives are required to achieve an average of at least \(5\) sales per day.

3. Find the least number of calls each day a representative should make to meet this requirement.[2]