Chapter 5.2, Problem 29AYU

Medicare Fines In an effort to reduce the number of hospital-acquired conditions (such as infection resulting from the hospital stay), Medicare officials score hospitals on a 10-point scale with a lower score representing a better patient track record. The federal government plans to reduce Medicare payments to those hospitals with the worst scores. The following data represent the scores received by Illinois hospitals.

Score	Frequency
1–1.9	3
2–2.9	12
3–3 9	16
4–4 9	23
5–5.9	23
6–6.9	21
7–7.9	17
8–8.9	5
9–10	5
Total	125
Source: Center for Medicare and Medicaid Services

1. a. Determine the probability that a randomly selected hospital in Illinois has a score between 5 and 5.9.
2. b. Determine the probability that a randomly selected hospital in Illinois has a score that is not between 5 and 5.9.
3. c. Determine the probability that a randomly selected hospital in Illinois has a score less than 9.
4. d. Suppose Medicare plans to reduce Medicare payments to any hospital with a score of 8 or higher. What is the probability a randomly selected hospital in Illinois will experience reduced Medicare payments? Interpret this result. Is it unusual?