Question

New patients arrive at the emergency room in Mercy Hospital at a mean arrival rate of 14.4 patients per hour.

a. What is the probability that no new patients will arrive at the emergency room within a 15-minute interval?

Do not round intermediate calculations. Round your answer to four decimal places.

Probability =

   

b. What is the probability that more than one new patient will arrive at the emergency room within a 15-minute interval?

Round intermediate probabilities to four decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.

Probability =

c. What is the probability that more than two new patients will arrive at the emergency room within a 15-minute interval?    

Round intermediate probabilities to four decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.

Probability =

d. On average, how many new patients to the emergency room will arrive every twelve minutes?

Round your answer to two decimal places.

new patients

Answer 1

a)

Here, λ = 3.6 and x = 0
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 0)
P(X = 0) = 3.6^0 * e^-3.6/0!
P(X = 0) = 0.0273
Ans: 0.0273

b)

Here, λ = 3.6 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 1) = 1 - P(X <= 1).
P(X > 1) = 1 - (3.6^0 * e^-3.6/0!) + (3.6^1 * e^-3.6/1!)
P(X > 1) = 1 - (0.0273 + 0.0984)
P(X > 1) = 1 - 0.1257 = 0.8743

c)

Here, λ = 3.6 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 2) = 1 - P(X <= 2).
P(X > 2) = 1 - (3.6^0 * e^-3.6/0!) + (3.6^1 * e^-3.6/1!) + (3.6^2 * e^-3.6/2!)
P(X > 2) = 1 - (0.0273 + 0.0984 + 0.1771)
P(X > 2) = 1 - 0.3028 = 0.6972

d)

New patients = (14.4 * 12)/60
= 2.88