$2025$ - $2026$ 学年 医学科学素养Ⅱ 练习2

基础医学专业课 线下练习题
2025.10.16, 不计分, 不作考勤

  1. Relationship between SCN levels and self-reported cigarettes smoked per week

    Self-reported cigarettes smoked in past week Number of students Percent with SCN ≥ 100 µg/mL
    None 1163 3.3
    1–4 70 4.3
    5–14 30 6.7
    15–24 27 29.6
    25–44 19 36.8
    45+ 23 65.2

    Suppose the self-reports are completely accurate and are representative of the number of eighth-grade students who smoke in the general community. We are considering using an SCN level ≥ 100 µg/mL as a test criterion for identifying cigarette smokers. Regard a student as positive if he or she smokes one or more cigarettes per week.

    1) What is the sensitivity of the test for light-smoking students (students who smoke ≤ 14 cigarettes per week)?

    2) What is the specificity of the test?

  2. Please calculate the standardized cure rate for hospital A and B.

    GROUP Hospital A Hospital B
    # of patients cure rate # of patients cure rate
    1 1000 700 0.7 100 90 0.9
    2 100 20 0.2 1000 400 0.4
    sum 1100 720 0.655 1100 490 0.445


  3. The probability of men with color blindness in a given population is 0.025. Suppose the ratio of men and women is 8:7. Now select a man randomly, what's the probability that he is color blind?

  4. The death probability of mice injected with a certain drug is 0.45. If 15 mice accepted the injection, what's the probability that at most 12 mice died? (You can use R program)

  5. There are six bacteria in 1 mL water from a pond. What's the probability that we detect 4 bacteria in 1 mL water?

  6. If calls to your cell phone are a Poisson process with a constant rate λ = 2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5-hour movie, your phone rings during that time?

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