Question

Mammograms Many women choose to have annual mammograms to screen for breast

cancer after age $40$. A mammogram isn’t foolproof. Sometimes the test suggests that a

woman has breast cancer when she really doesn’t (a “false positive”). Other times the test

says that a woman doesn’t have breast cancer when she actually does (a “false negative”).

Suppose the false negative rate for a mammogram is $0.10.$

a. Explain what this probability means.

b. Which is a more serious error in this case: a false positive or a false negative? Justify

your answer.

Short answer

a) The probability of the mammogram's false-negative rate must be interpreted.

b) This probability might be interpreted as the percentage of false-negative findings in a large number of trials.

Step-by-step solution

Part (a) Step 1: Given information

We have to tell what this probability means.

Part (a) Step 2: Explanation

• The probability of the mammogram's false-negative rate must be interpreted.
• In this problem, the chance of a mammography false-negative rate is given$0.10$

Part (b) Step 1: Given information

We have to tell which is a more serious error in this case

Part (b) Step 2: Explanation

• This probability might be interpreted as the percentage of false-negative findings in a large number of trials.
• As a result, if we use mammography on a large number of women with cancer, approximate) of them will have a$0.10\%$ negative test.