4. According to a recent survey, an average worker is absent on nine days during the year for various reasons (e.g., illness, bereavement). Assuming 365 days in a year, 25 holidays, and ten bank holidays, the average worker has 230 working days per year. Suppose that worker absenteeism is a good proxy for student absenteeism. Out of the 400 registered for ECU11022 in 2022, 32 students were absent from the final test. a) Let X denote a random variable that captures the number of students taking ECU11022 absent on a given day. Provide an expression for the distribution ofX. b) What is the proportion of students absent on a given day? c) Would you say that the number of absent students during the day of the test was atypical? Explain your answer with statistical arguments.