A newly developed blood test to detect breast cancer is being evaluated by a private company. The company tries out the test on 1000 women with known breast cancer, and of these, 900 have positive test results. The company tests 1000 women without breast cancer, and 20 of these test positive.

a)What are the sensitivity and specificity of the test?

b)Public health officials want to use this blood test for women who are older than 50 years old. The prevalence of breast cancer in this population is 5 per 1000. What is the overall probability of a positive test result in this population?

c)Given that a woman receives a positive test result, what is the probability she truly has breast cancer?

d) In a sample of size 20, what is the probability distribution for the number of positive tests? What is the expected number of positive tests? Explain.