Question 1: Probability of Pre-term Delivery

Total pre-term deliveries: 520 Total women: 6000

Probability of pre-term delivery: 520 / 6000 = 0.0867

Question 2: Probability of BMI Less than 30

Total women with BMI less than 30: 5020 Total women: 6000

Probability of BMI less than 30: 5020 / 6000 = 0.8367

Question 3: Probability of BMI Less than 30 and Pre-term Delivery

Women with BMI less than 30 and pre-term delivery: 320 Total women: 6000

Probability of BMI less than 30 and pre-term delivery: 320 / 6000 = 0.0533

Question 4: Proportion of Women with BMI Greater than 35 Delivering Full-term

Women with BMI greater than 35 and full-term delivery: 300 Total women with BMI greater than 35: 420

Proportion: 300 / 420 = 0.7143

Questions 5-8: Diagnostic Test Evaluation

Question 5: Sensitivity

Sensitivity: True positives / (True positives + False negatives) = 35 / (35 + 5) = 0.875

Interpretation: The test correctly identifies 87.5% of individuals who are truly HIV-positive.

Question 6: Specificity

Specificity: True negatives / (True negatives + False positives) = 50 / (50 + 10) = 0.8333

Interpretation: The test correctly identifies 83.33% of individuals who are truly HIV-negative.

Question 7: Positive Predictive Value (PPV)

PPV: True positives / (True positives + False positives) = 35 / (35 + 10) = 0.7778

Interpretation: If a person tests positive, there is a 77.78% chance that they are truly HIV-positive.

Question 8: Negative Predictive Value (NPV)

NPV: True negatives / (True negatives + False negatives) = 50 / (50 + 5) = 0.9091

Interpretation: If a person tests negative, there is a 90.91% chance that they are truly HIV-negative.

Questions 9-11: Short Essay

Question 9: Binomial vs. Normal Distributions

Binomial Distribution:

• Used for discrete random variables (e.g., number of successes in a fixed number of trials).
• Parameters: n (number of trials), p (probability of success in a single trial).
• Example in public health: The number of people who develop flu in a sample of 100 individuals exposed to the virus.

Normal Distribution:

• Used for continuous random variables (e.g., height, weight).
• Parameters: mean (μ) and standard deviation (σ).
• Example in public health: The distribution of birth weights in a population of newborns.

Question 10: Probability Laws and Screening Tests

Probability laws and concepts are used in the evaluation of screening tests and diagnostic criteria to assess their accuracy and effectiveness. For example:

• Sensitivity: The probability that a test will correctly identify individuals with a disease.
• Specificity: The probability that a test will correctly identify individuals without a disease.
• Positive predictive value: The probability that a positive test result indicates the presence of the disease.
• Negative predictive value: The probability that a negative test result indicates the absence of the disease.

By understanding these concepts, public health professionals can evaluate the performance of screening tests and make informed decisions about their use.

Question 11: Random Experiment vs. Trial

Random Experiment: A procedure with uncertain outcomes that can be repeated under identical conditions.

• Example: Tossing a coin to determine heads or tails.

Trial: A single observation or outcome of a random experiment.

• Example: One toss of a coin.

In public health, random experiments are used to collect data and assess the effectiveness of interventions. For example, a randomized controlled trial might be conducted to evaluate the efficacy of a new vaccine. Trials are the individual observations within the experiment.