At an outpatient mental health clinic, appointment cancellations occur at a mean

Question

At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 2.0 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday. (a) Justify the use of the Poisson model. Cancellations are independent and similar to arrivals. O Cancellations are not independent. Most likely cancellations arrive independently. (b) What is the probability that no cancellations will occur on a particular Wednesday? (Round your answer to 4 decimal places.) Probability (c) What is the probability that one cancellation will occur on a particular Wednesday? (Round your answer to 4 decimal places.) Prsabiliy (d) What is the probability that more than three cancellations will occur on a particular Wednesday? (Round your answer to 4 decimal places.) Probability (e) What is the probability that three or more cancellations will occur on a particular Wednesday? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

A) Option-A

B) P(X = 0) = e-2 * 20 / 0! = 0.1353

C) P(X = 1) = e-2 * 21 / 1! = 0.2707

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

= 1 - (0.1353 + 0.2707 + e-2 * 22 / 2! + e-2 * 23 / 3!)

= 1 - 0.8571

= 0.1429

E) P(X > 3) = P(X = 3) + P(X > 3)

= e-2 * 23 / 3! + 0.1429

= 0.3233

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