An article in Vaccine [“Modeling the Effects of Influenza Vaccination of Health Care Workers in Hospital Departments” (2009, Vol.27(44), pp. 6261–6267)] considered the immunization of healthcare workers to reduce the hazard rate of influenza virus infection for patients in regular hospital departments. In this analysis, each patient’s length of stay in the department is taken as exponentially distributed with a mean of 7.0 days.

(a) What is the probability that a patient stays in hospital for less than 5.5 days?

(b) What is the probability that a patient stays in hospital for more than 10.0 days if the patient has currently stayed for 7.0 days?

(c) Determine the mean length of stay such that the probability is 0.9 that a patient stays in the hospital less than 6.0 days.