The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who takes a mammography to screen for breast cancer: 0.8 Positive Cancer 0.0286 Negative 0.2 M ammography 0.1 Positive 0.9714 No cancer Negative 0.9 (a) A true positive happens when someone getting a mammography has cancer and receives a positive test result. What percent of women in their 50s taking a screening mammography receive a true positive? (b) A false positive happens when someone getting a mammography does not have cancer and receives a positive test. What percent of women in their 50s taking a screening mammography receive a false positive? (c) What percent of women in their 50s taking a screening mammography receive a positive test result?
The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who takes a mammography to screen for breast cancer: 0.8 Positive Cancer 0.0286 Negative 0.2 M ammography 0.1 Positive 0.9714 No cancer Negative 0.9 (a) A true positive happens when someone getting a mammography has cancer and receives a positive test result. What percent of women in their 50s taking a screening mammography receive a true positive? (b) A false positive happens when someone getting a mammography does not have cancer and receives a positive test. What percent of women in their 50s taking a screening mammography receive a false positive? (c) What percent of women in their 50s taking a screening mammography receive a positive test result?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:The incidence of breast cancer varies depending on a woman's age. The National
Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who
takes a mammography to screen for breast cancer:
0.8
Positive
Cancer
0.0286
Negative
0.2
M ammography
0.1
0.9714
Positive
No cancer
Negative
0.9
(a) A true positive happens when someone getting a mammography has cancer and receives a
positive test result. What percent of women in their 50s taking a screening mammography
receive a true positive?
(b) A false positive happens when someone getting a mam
receives a positive test. What percent of women in their 50s taking a screening mammography
receive a false positive?
ammography does not have cancer and
(c) What percent of women in their 50s taking a screening mammography receive a positive test
result?
(d) If a randomly chosen woman in her 50s taking the mam
test result, the probability that she indeed has breast cancer is the positive predicted value, PPV =
P(Cancer | Positive test). What is the PPV for this age group?
ammography screening test gets a positive
%3D
(e) The specificity of a diagnosis test is its ability to appropriately give a negative result when a
person tested doesn't have the disease, P(Negative test | No cancer). What is the specificity of
mammography screening test?
2
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