Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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 large-scale study of elderly icu patients, the average length of stay in the icu is days (critical care medicine journal article). assume that this length of stay in the icu has an exponential distribution. do not round intermediate calculations.

Sagot :

abiolataiwo2015

a. Probability that the length of stay in the ICU is one day or less is:0.2614.

b. Probability that the length of stay in the ICU is between two and three days is:0.1426

c. Probability that the length of stay in the ICU is more than five days is:0.2198.

Probability

a. Probabilty of one day or less.

Using this formula

P(X≤1)=1-e^-ux

Since mean is 3.3 the decay parameter is:

u=1/3.3

Hence:

P(X≤1)=1-e^-1/3.3

P(X≤1)=1-e^-0.3030

P(X≤1)=1-0.7385991

P(X≤1)=0.2614

b. Probability of two and three days.

P(X≤2)=1-e^-ux

P(X≤2)=1-e^-2/3.3

P(X≤2)=1-e^-0.60606

P(X≤2)=1-0.54549589

P(X≤2)=0.45450

P(X≤3)=1-e^-ux

P(X≤3)=1-e^-3/3.3

P(X≤3)=1-e^-0.909091

P(X≤3)=1-0.402890

P(X≤3)=0.59711

Hence:

P(2≤X≤3)=0.59711-0.45450

P(2≤X≤3)=0.1426

c. Probability of more than 5 days.

P(X≤5)=e^-ux

P(X≤5)=e^-5/3.3

P(X≤5)=e^-1.515152

P(X≤5)=0.219775

P(X≤5)=0.2198 (Approximately)

Inconclusion the probability that the length of stay in the ICU is one day or less is:0.2614.

Learn more about probability here:https://brainly.com/question/25710880

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.