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 1.7 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 not independent Most likely cancellations arrive independently Cancellations are independent and similar to arrivals (b) What is the probability that no cancellations will occur on a particular Wednesday? (Round your answer to 4 decimal places.) Probability .1826 (c) What is the probability that one cancellations will occur on a particular wednesday? (Round your answer to 4 decimal places.) Probability .3105 (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 four or more cancellations will occur on a particular wednesday? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

a)

Cancellations are independent and similar to arrivals [ANSWER]

*************************

b)

Note that the probability of x successes is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    1.7      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.182683524 [ANSWER]

***********************

c)

Note that the probability of x successes is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    1.7      
          
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.310561991 [ANSWER]

*************************

d)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    1.7      
          
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   3   ) =    0.906810566
          
Thus, the probability of at least   4   successes is  
          
P(more than   3   ) =    0.093189434 [ANSWER]

***************************

e)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    1.7      
          
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.906810566
          
Thus, the probability of at least   4   successes is  
          
P(at least   4   ) =    0.093189434 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.