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Sagot :
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
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