1. The probability of event A is 0.85: P(A) = 0.85.The probability of event B is 0.35: P(B) = 0.35.What is the smallest value that the joint probability of of A and B - P(AandB) - can take? (Hint: Consider the rule of addition and the range of possible values the intersection can validly take)
2. 0.00
3. 0.10
4. 0.20
5. 0.29

2.

On a randomly selected day, 90 high school students were tardy and 120 were in violation of the dress code.If the high school has 600 students, how many students would have to have been both tardy and in violation of the dress code for these two events to be independent?

1. 0
2. 18
3. 27
4. 30

3.

1. At a company of 940 employees, during open enrollment, 400 employees signed up for health plan A, 25 for health plan B, 120 for health plan C, 300 for health plan D, 55 for health plan E, and 40 for health plan F.What is the probability that a randomly selected employee did not sign up for health plan B?
2. 0.68
3. 0.92
4. 0.43
5. 0.97

4.

At a university, 15% of all students signed up for the campus meal plan AND purchased an all-access athletics pass.66% of all students signed up for the campus meal plan.What is the probability that a student purchased the all-access athletics pass given that he/she signed up for the campus meal plan?

1. 0.10
2. 0.23
3. 0.29
4. 0.51

5.

A post-discharge survey was administered to emergency room patients.It found that45% of all patients visited for a condition that was non-emergent.Also, among patients that were visiting for a non-emergentcondition, 16% patients expressed satisfaction with the length of time spent in the waiting room.Among ALL patients, what percentage visited the emergency room with a non-emergent condition AND expressed satisfaction with the length of time spent in the waiting room?

1. 6.0%
2. 7.2%
3. 29.0%
4. 35.6%

6.

1. The probability that a client will be home when a home health nurse visits is 0.70.Assuming that visits to different clients are independent of each other, what is the probability that a client will be home at the nurse's first visit and a client will be home at the nurse's second visit?
2. 0.00
3. 0.49
4. 0.50
5. 0.64

7.

1. A company has developed an automatic retinal scanner for the detection of overexposure to a carcinogenic industrial solvent.The company tested the scanner by recruiting 120 individuals known to be overexposed to the solvent and 200 individuals known to be not overexposed to the solvent.The retinal scanner was positive for overexposure in 108 of the overexposed individuals.The retinal scanner was positive for overexposure in 48 of the 200 not overexposed individuals.

What is the sensitivity of the retinal scanner?

1. 0.76
2. 0.90
3. 0.92
4. 0.96

8.

1. What is the specificity of the retinal scanner?
2. 0.76
3. 0.90
4. 0.92
5. 0.96

9.

1. A city is considering using the retinal scanner to screen residents living near an industrial plant where the carcinogenic industrial solvent is manufactured.The prevalence of overexposure in this population is known to be 0.10.What will be the positive predictive value (PPV) of the retinal scanner in this population?
2. 0.12
3. 0.29
4. 0.38
5. 0.69

10.

1. The same city is also planning on screening residents living far from the industrial plant.The prevalence of overexposure in this population is known to be 0.02.What will be the positive predictive value (PPV) of the retinal scanner in this population?
2. 0.018
3. 0.02
4. 0.07
5. 0.69

11.

1. The owner of the industrial plant is considering using the retinal scanner to screen employees at high risk for overexposure.The prevalence of overexposure among high risk employees is 0.05.What will be the negative predictive value (NPV) of the retinal scanner in this population?
2. 0.16
3. 0.72
4. 0.95
5. 0.99

12.

1. The retinal scanner produces a continuous measurement, called the OE Index.When the OE Index is large, the individual being measured is more likely to have been overexposed.The company that developed the retinal scanner conducted a study to determine the best threshold for the OE index above which patients would be classified as over-exposed to the solvent.The graph on the first page of the file "Week4HW_ROCCurve.pdf" contains the ROC curve for the OE index produced from the data in this study.
2. Judging from the ROC curve, what is the most likely value for the area under the curve (AUC) for the OE index? (Hint: No calculation here - you should be able to "reason" your way to the answer based on the properties of AUC).
3. 0.42
4. 0.50
5. 0.82
6. 0.99

13.

1. The labeled point in the ROC curve for the OE Index indicates that the optimal cutpoint for the OE index is 34.95, with specificity 0.94 and sensitivity 0.49.Which of the following describes the proper use of this cutpoint?
2. If the OE Index is less than34.95, then the individual is over-exposed.If not, then the individual is not over-exposed.
3. If the OE Index is greater than34.95, then the individual is over-exposed.If not, then the individual is not over-exposed.

14.

1. In developing the retinal scanner, the developers considered a second continuous measurement - called the RS Index - for classifying individuals as over-exposed or not over-exposed.The ROC curve for the RS Index is on the second page of the file "Week4HW_ROCCurve.pdf".TRUE or FALSE:The retinal scanner would do a better job of accurately classifying individuals as over-exposed or not over-exposed if the RS Index were used rather than OE Index.
2. True
3. False