3. The number of claims made to the home insurance department of an insurance company follows a Poisson distribution with mean 4 per day.
- Find the probability that more than 11 claims are made in a 2 -day period.
The number of claims made in a day to the pet insurance department of the same company follows a Poisson distribution with parameter \(\lambda\). An insurance company worker notices that the probability of two claims being made in a day is three times the probability of four claims being made in a day.
- Determine the value of \(\lambda\).
The car insurance department models the length of time between claims for drivers aged 17 to 21 as an exponential distribution with mean 10 months. Rachel is 17 years old and has just passed her test. Her father says he will give her the car that they share if she does not make a claim in the first 12 months.
- What is the probability that her father gives her the car?