3. The sales staff at an insurance company make house calls to prospective clients. Past records show that \(30 \%\) of the people visited will take out a new policy with the company.
On a particular day, one salesperson visits 8 people. Find the probability that, of these,
- exactly 2 take out new policies,
- more than 4 take out new policies.
The company awards a bonus to any salesperson who sells more than 50 policies in a month.
- Using a suitable approximation, find the probability that a salesperson gets a bonus in a month in which he visits 150 prospective clients.
(5 marks)