A hospital researcher is interested in the number of timesXthat the average post-op patient will ringthe nurse during a 12-hour shift.Based on a large sample of patient records, the following probability distribution forXwas obtained:

XP(X)

00.0610.1420.223?40.1850.08

Use this to fill in the blank and answer the following questions; give your answers accurate to two decimal places.

a)Find the probability that a randomly selected patient rings the nurse exactly 3 times.

b) Calculate the probability that a patient rings the nurse at most 2 times.

c) If a patient is selected at random, what is the expected number of times that he/she will ring the nurse?