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4.8.1: Practice Problems Corequisite N.8 and N.9

  • Page ID
    148613
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    A teacher has collected data on the grades his students received in his morning and afternoon classes. The following tables show two different ways to represent the same data as percentages.

    Table 1
      Grade A Grade B Grade C Grade D Grade F
    Morning Class 12.5% 25.0% 37.5% 6.3% 18.7%
    Afternoon Class 14.3% 20.0% 37.1% 8.6% 20.0%
    Table 2
      Grade A Grade B Grade C Grade D Grade F
    Morning Class 44.4% 53.3% 48.0% 40.0% 46.2%
    Afternoon Class 55.6% 46.7% 52.0% 60.0% 53.8%

    (1) What percentage of the students who received an “B” is in the morning class? Write your answer in a complete sentence.

    (2) What percentage of the students in the morning class received an “B”? Write your answer in a complete sentence.

    (3) What are the reference values in Table 1?

    (i) The number of students in a certain class.

    (ii) The number of students who earned a certain grade.

    (iii) The number of students in a certain class who earned a certain grade.

    (iv) The total number of students in both classes.

    (4) What are the reference values in Table 2?

    (i) The number of students in a certain class.

    (ii) The number of students who earned a certain grade.

    (iii) The number of students in a certain class who earned a certain grade.

    (iv) The total number of students in both classes.

    A test is administered to 500 athletes to determine if they are using performance-enhancing drugs (PEDs). It is assumed that a positive test result indicates that the athlete is using PEDs, and a negative test result indicates that the athlete is not using PEDs. However, this test is not 100% accurate, so some errors occur. The following table shows the test results for a group of athletes.

      Athletes Using PEDs Athletes Not Using PEDs Total
    Positive Test Result 90 4 94
    Negative Test Result 10 396 406
    Total 100 400 500

    Use the information in the table to answer the following questions.

    (5) How many athletes are using PEDs?

    (6) If an athlete is using PEDs, which of the following describes the chance that this test will give a positive result? There may be more than one correct answer.

    (i) 9%

    (ii) 90%

    (iii) 9 out of 100

    (iv) 90 out of 100

    (7) What is the chance of the test giving a negative result for an athlete using PEDs?

    (8) If an athlete is not using PEDs, what is the chance that this test will give a negative result?

    (i) 39.6%

    (ii) 99%

    (iii) 4 out of 396

    (iv) 4 out of 400

    (9) What is the chance of the test giving a positive result for an athlete not using PEDs?

    A hospital tracks the number of cases (patients) that come into its Emergency Room during each eight-hour shift. The cases are listed in categories based on the severity of the illness or injury. The categories from least severe to most severe are: stable, serious, and critical. The following table gives the data for a week.

    Shift Stable Serious Critical Total
    8:00 a.m. – 3:59 p.m. 250 120 45 415
    4:00 p.m. – 11:59 p.m. 270 230 105  
    12:00 a.m. – 7:59 a.m.   175 95 460
    Total 710   245 1480

    (10) What is the total number of cases for the 4:00 p.m. – 11:59 p.m. shift?

    (11) What is the number of stable cases for the 12:00 a.m. – 7:59 a.m. shift?

    (12) What is the total number of serious cases across all shifts?

    A nursing supervisor ranks the shifts based on two different criteria. Which shift received the highest percentage of the total critical cases? For Questions 13-15, find the percentage of critical cases for each shift. Round to the nearest one percent.

    Shift Percentage of Total Critical Cases
    8:00 a.m. – 3:59 p.m. (13)
    4:00 p.m. – 11:59 p.m. (14)
    12:00 a.m. – 7:59 a.m. (15)

    (16) Which shift received the highest percentage of the total critical cases? Rank the shifts from highest to lowest.

    Now let's explore which shift has the highest percentage of critical cases compared to that shift’s total cases. Round to the nearest one percent.

    (17) 8:00 a.m. – 3:59 p.m.

    (18) 4:00 p.m. – 11:59 p.m.

    (19) 12:00 a.m. – 7:59 a.m.

    (20) Rank the shifts from highest to lowest.

    (21) Which of the following conclusions could be drawn?

    (i) The highest number and the highest ratio of experienced nurses should be scheduled during the 12:00 a.m. to 7:59 a.m. shift.

    (ii) The highest number of experienced nurses should be scheduled during the 4:00 p.m. to 11:59 p.m. shift. The highest ratio of experienced nurses should be scheduled during the 8:00 a.m. to 3:59 p.m. shift.

    (iii) The highest number and the highest ratio of experienced nurses should be scheduled during the 4:00 p.m. to 11:59 p.m. shift.

    (iv) The highest number of experienced nurses should be scheduled during the 12:00 a.m. to 7:59 a.m. shift. The highest ratio of experienced nurses should be scheduled during the 4:00 p.m. to 11:59 p.m. shift.

    (22) Given the following statistics, rank the risk of having a child with diabetes with the highest risk on top and lowest risk on the bottom.

    In general, if you are a man with type-1 diabetes, the odds of your child getting diabetes are 1 in 17. If you are a woman with type-1 diabetes and your child was born before you were 25, your child's risk is 1 in 25; if your child was born after you turned 25, your child's risk is 1 in 100.

    Rank the risk of having a child with diabetes from 1 (highest risk) to 3 (lowest risk).

    ___ Mother with type-1 diabetes who gave birth after turning 25

    ___ Father with type-1 diabetes

    ___ Mother with type-1 diabetes who gave birth before turning 25

    Mark each statement true or false.

    (23) A man with type-1 diabetes has a child. The probability that the child will also have diabetes is about 6%.

    (i) True (ii) False

    (24) A 20 year-old woman with type-1 diabetes has a child. The probability that the child will also have diabetes is about 25%.

    (i) True (ii) False

    (25) A 30-year-old woman with type-1 diabetes has a child. The probability that the child will also have diabetes is about 1%.

    (i) True (ii) False


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