A physiotherapist has a patient doing some slow jogging on a treadmill and sets the timer for 27 minutes. Suppose the speed needs to be adjusted when there is 11 minutes left to go. A little while later, the physiotherapist's assistant comes over to check on the patient, not knowing how much time is left on the treadmill.

a) What is the probability that the assistant will need to adjust the speed of the treadmill? [1 mark]

b) How much time would the assistant expect to be remaining on the timer? [1 mark]

c) Compute the variance for this situation. [1 mark]