6. A doctor expects to see, on average, 1 patient per week with a particular disease.
- Suggest a suitable model for the distribution of the number of times per week that the doctor sees a patient with the disease. Give a reason for your answer.
- Using your model, find the probability that the doctor sees more than 3 patients with the disease in a 4 week period.
The doctor decides to send information to his patients to try to reduce the number of patients he sees with the disease. In the first 6 weeks after the information is sent out, the doctor sees 2 patients with the disease.
- Test, at the \(5 \%\) level of significance, whether or not there is reason to believe that sending the information has reduced the number of times the doctor sees patients with the disease. State your hypotheses clearly.
Medical research into the nature of the disease discovers that it can be passed from one patient to another.
- Explain whether or not this research supports your choice of model. Give a reason for your answer.