Question: A medical information specialist knows that 40% of the geriatric patients seen at the medical practice where she works get flu shots annually.

a) What is the likelihood that she must review eight randomly selected files where patients did not receive flu shots before she finds one where the patient did receive flu shots annually?

b) What is the chance that, if twelve files were reviewed, at least half would show that their patients received flu shots annually?

c) What is the probability that, in order to find four medical records noting that flu shots were given to those patients annually, exactly twenty files must be selected? [COMMENTS & HINTS: The fourth shot occurs precisely in the twentieth file, not earlier.]

d) If 625 patient files are randomly reviewed, what is the expected number of patients who received flu shots and what is the variance?