Support requests arrive at a software company at the rate of 1 every 10 minutes.

Question

Support requests arrive at a software company at the rate of 1 every 10 minutes. Assume that the requests arrive as events in a Poisson process. What is the expected number of requests in an hour? Give an exact answer. What is the probability that the number of requests in an hour is between 8 and 10 inclusive? Give your answer to four decimal places. What is the expected number of requests in a 10 hour work day? Give an exact answer. What is the probability that the number of requests in a 10 hour work day is between 68 and 72 inclusive? Give your answer to four decimal places. What is the standard deviation of the number of requests in a 10 hour work day? Give your answer to four decimal places.

Explanation / Answer

a)

E(x per hour) = (1 request/10 min)(60 min) = 6 requests [ANSWER]

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b)

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    8      
x2 =    10      
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    6      
          
          
Then          
          
P(at most    7   ) =    0.74397976
P(at most    10   ) =    0.957379076
          
Thus,          
          
P(between x1 and x2) =    0.213399316   [ANSWER]

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c)

As there are 6 requests/hr, then for 10 hours, that is

6*10 = 60 requests [ANSWER]

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d)

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    68      
x2 =    72      
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    60      
          
          
Then          
          
P(at most    67   ) =    0.834022889
P(at most    72   ) =    0.943282728
          
Thus,          
          
P(between x1 and x2) =    0.109259839   [ANSWER]

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e)

As

standard deviation = sqrt(mean)

Then as mean = 60,

standard deviation = sqrt(60) = 7.745966692 [ANSWER]

  
  

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