Support requests arrive at a software company at the rate of 1 every 30 minutes.

Question

Support requests arrive at a software company at the rate of 1 every 30 minutes. Assume that the requests arrive as events in a Poissor process a. What is the expected number of requests in an hour? Give an exact answer. 2 b. What is the probability that the number of requests in an hour is between 2 and 4 inclusive? Give your answer to four decimal places. 5413 c. What is the expected number of requests in a 10 hour work day? Give an exact answer. 2 d. What is the probability that the number of requests in a 10 hour work day is between 20 and 28 inclusive? Give your answer to four decimal places. e. What is the standard deviation of the number of requests in a 10 hour work day? Give your answer to four decimal places. 4.4721

Explanation / Answer

Solution :
Given that ? = 1 per 30 min
= 1 per 0.5 hour

c. Expect 20 in 10 hours

=> ? = 2 per 1 hour

For 10 hours ,
=> ? = 2*10 = 20 per 10 hours

d. ? = 20 per 10 hours

P(20 <= x <= 28) = P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25) + P(x = 26) + P(x = 27) + P(x = 28)

= 0.0888 + 0.0846 + 0.0769 + 0.0669 + 0.0557 + 0.0446 + 0.0343 + 0.0254 + 0.0182

= 0.4954

Formula : for poisson distribution P(x,?) = (e^(-?) * ?^x)/x!

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