At an outpatient mental health clinic appointment cancellati

At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 2.7 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday.

a. What is the probability that no cancellations will occur on a particular Wednesday? (Round your answer to 4 decimal places.)

b. What is the probability that one cancellations will occur on a particular wednesday? (Round your answer to 4 decimal places.)

c. What is the probability that more than three cancellations will occur on a particular wednesday? (Round your answer to 4 decimal places.)

d. What is the probability that five or more cancellations will occur on a particular wednesday? (Round your answer to 4 decimal places.)

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X = 0 ) = e ^-2.7 * 2.7^0 / 0! = 0.0672

b)
P( X = 1 ) = e ^-2.7 * 2.7^1 / 1! = 0.1815

c)
P( X < 3) = P(X=2) + P(X=1) + P(X=0) +   
= e^-2.7 * 0 ^ 2 / 2! + e^-2.7 * ^ 1 / 1! + e^-2.7 * ^ 0 / 0!
= 0.4936
P( X > = 3 ) = 1 - P (X < 3) = 0.5064

d)

P( X < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-2.7 * 0 ^ 4 / 4! + e^-2.7 * ^ 3 / 3! + e^-2.7 * ^ 2 / 2! + e^-2.7 * ^ 1 / 1! + e^-2.7 * ^ 0 / 0!
= 0.8629
P( X > = 5 ) = 1 - P (X < 5) = 0.1371