Medical tests are frequently used to decide whether a person has a particular illness. The sensitivity of a test is the probability that a person having the illness will test positive; the specificity of a test is the probability that a person not having the illness will test negative. According to the National Cancer Institute and the Surveillance Epidemiology and End Results Fact Sheet, roughly 7.9 per 100,000 women have cancer of the cervix. A Pap test, or Papanicolaou test, is a screening test used to detect precancerous and cancerous cells in the cervix. The specificity of the Pap test is 98% and the sensitivity of the Pap test is 51% according to the Alliance for Cervical Cancer Protection.
a. Interpret the sensitivity and specificity of this test in terms of percentages.
b. Determine the probability that a randomly selected female tests positive.
c. Determine the probability that a female testing positive actually has cervical cancer.
d. Interpret your answers from parts (b) and (c) in terms of percentages.