A physician sees many different kinds of patients, and thus the time spent with each patient varies. Let X be the time spent with a patient in minutes. From historical data, X is known to be uniformly distributed between 15 and 40 minutes.

a) What is the standard deviation of the time spent with a patient?

b) What is the likelihood that the physician will spend less than 35 minutes with a patient?

c) A patient has an appointment to see the physician at 8AM on a particular day. When should the second patient be scheduled so that there is only a 15% chance s/he will have to wait before before being seen by the physician? [e.g. if the appointment for the second patient is 8:15AM, there is a 100% chance the second patient will have to wait]