richaeviney
25.11.2021 •
Mathematics
Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.
a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?
b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?
c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?
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Ответ:
Step-by-step explanation:
1. The first step in problem solving is to look at the given information. Here, you can see that each number in the sequence is 2 less than the one before it.
In the expression ...
an = an-1 - 2
the term an-1 means the previous term, the term just before term an. So, this equation means the term of the sequence is 2 less than the one before it. Since this matches the description of the sequence, this recursive relation is part of the correct answer. (The other part is the definition of the first term of the sequence: a1 = 8.)
The recursive definition is ...
__
2. The given sequence has first term a1 = -3, and common difference d = 4. That is, each term is 4 more than the previous one. The explicit formula for an arithmetic sequence is ...
an = a1 +d(n -1)
Filling in the given values gives you the explicit formula ...