Pap Tests. 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 specicity 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 EndResults 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 specicity 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 specicity 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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Pap Tests. Medical tests are frequently used to decide whether a person has a particular illness. The sensitivity of a test is the
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 specicity 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 specicity 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.
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