Examkin

Soru

Zorluk: OrtaNumerical, Proportion, and Statistical Inferences

In 2024, Meridian Health System operated 10 general hospitals. In 2025, to lower hospital-acquired infection rates, Meridian introduced stricter hygiene protocols across all 10 hospitals. By the end of 2025, the proportion of admitted patients who contracted a hospital-acquired infection at Meridian hospitals fell from 4.0 percent in 2024 to 2.5 percent in 2025. During that same period, the total number of patient admissions across the 10 hospitals increased by 80 percent.

If the statements above are true, which of the following must also be true on the basis of them?

  1. The absolute number of patients who contracted a hospital-acquired infection at Meridian hospitals was higher in 2025 than in 2024.Cevap
  2. B
    The absolute number of hospital-acquired infections recorded across Meridian hospitals decreased by 37.5 percent between 2024 and 2025.
  3. C
    At least one of the 10 individual hospitals in the Meridian system experienced an increase in its specific rate of hospital-acquired infections.
  4. D
    The new hygiene protocols failed to lower the risk of any individual admitted patient contracting a hospital-acquired infection.
  5. E
    The average duration of stay for patients who contracted an infection was longer in 2025 than in 2024.

Cevap

The total absolute number of patients who contracted a hospital-acquired infection at Meridian hospitals was higher in 2025 than in 2024.
The correct response logically follows from combining the percentage rate with total volume changes. In 2024, infections equaled 4.0% of total admissions NN (0.04N0.04N). In 2025, admissions grew to 1.80N1.80N, and 2.5% of 1.80N1.80N equals 0.045N0.045N. Because 0.045N0.045N is greater than 0.04N0.04N, the total number of infected patients was higher in 2025.

Adım Adım Çözüm

1
Define base variables from the premise.
Let NN be the total number of patient admissions in 2024. The number of infected patients in 2024 is 0.04×N0.04 \times N.
Establishing raw counts relative to the baseline allows mathematical comparison.
2
Calculate the total admissions and infection count for 2025.
2025 admissions = 1.80×N1.80 \times N. The number of infected patients in 2025 is 0.025×(1.80×N)=0.045×N0.025 \times (1.80 \times N) = 0.045 \times N.
Applying the 80 percent increase in total volume alongside the 2.5 percent rate yields the new absolute count.
3
Compare the 2024 and 2025 absolute infection counts.
0.045×N>0.040×N0.045 \times N > 0.040 \times N, meaning the absolute number of infections increased.
Since 0.045>0.0400.045 > 0.040, it is mathematically necessary that more total patients contracted infections in 2025 than in 2024.

Anahtar Kavram

Disambiguating proportion/percentage changes from changes in absolute total volume when base values change.
Bu soruyu puanla

Konular

Numerical, Proportion, and Statistical Inferences

Bu konudan daha fazla soru