Question

At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.3 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday.

(d)

What is the probability that more than three cancellations will occur on a particular Wednesday?

(e)	What is the probability that three or more cancellations will occur on a particular Wednesday?

Answer 1

Solution :

Given that ,

mean = = 1.3

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

(d)

P(X > 3) = 1 - P(X 3)

= 1 - P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 1 - [(e^-1.3 * 1.3⁰⁾ / 0! + (e^-1.3 * 1.3¹⁾ / 1! + (e^-1.3 * 1.3²⁾ / 2! + (e^-1.3 * 1.3³⁾ / 3!]

= 1 - 0.9569

= 0.0431

Probability = 0.0431

(e)

P(X 3) = 1 - P(X < 3)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2) ]

= 1 - [(e^-1.3 * 1.3⁰⁾ / 0! + (e^-1.3 * 1.3¹⁾ / 1! + (e^-1.3 * 1.3²⁾ / 2!]

= 1 - 0.8571

= 0.1429

Probability = 0.1429