Question

Intensive care unit (ICUS) generally treat the sidest 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 Suppose that a large-scale study of elderly ICU patients shows that the average length of stay in the ICU is 3.5 days. Assume that this length of stay in the ICU has an exponential distribution (Round your answers to four decimal places.) (a) What is the probability that the length of stay in the ICU is one day or less? (b) What is the probability that the length of stay in the ICU is between two and three days? (c) What is the probability that the length of stay in the ICU is more than five days?

Answer 1

Given,

$\lambda$ = 3.5

Consider exponential distribution P(X <= x) = 1 - e^(-x/$\lambda$)

a)

To give the probability that the length of stay in the ICU is one day or less

P(X <= 1) = 1 - e^(-1/3.5)

= 0.2485

b)

To give the probability that the length of stay in the ICU is between two and three days

P(2 <= X <= 3) = P(X <= 3) - P(X <= 2)

= (1 - e^(-3/3.5)) - (1 - e^(-2/3.5))

= 0.5756 - 0.4353

= 0.1403

c)

To give the probability that the length of stay in the ICU is more than five days

P(X > 5) = e^(-5/3.5)

= 0.2351