It has been estimated that 5% of people who are hospitalized pick up infections while in the hospital, and that 2.2 million people a year get sick and 88,000 die because of these infections. Experts advise patients to be sure that health care personnel have washed their hands, to select surgeons with higher levels of experience, and to minimize the amount of time that they are treated with catheterization.
Grove Tree Mountain Hospital anticipates admitting 100 patients this month for surgical and other treatments. Suppose that 14 of the patients in the sample actually end up getting a hospital-borne infection. Treating the 100 patients as a random sample of all hospital patients, and applying the infection rate cited above, what is the probability that a typical hospital would have 14 or more infections in a sample of this size?
Considering this probability, comment on whether Grove Tree Mountain might not be a typical hospital in terms of its patients' likelihood of picking up an infection.