6. The scheduling manager for an electricity supply company knows that there are on average 12...

 

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6. The scheduling manager for an electricity supply company knows that there are on average 12 emergency calls regarding power failures per month. Assume that the number of emergency calls per month can be modelled by a Poisson process and that there are 30 days in every month. (a) What is the probability that the company receives no emergency calls in a particular month? (b) What is the probability that at least 3 emergency calls in a particular month? (c) What is the expected number of emergency calls in a particular month? What is the variance? (d) Suppose that the company can handle a maximum of two emergency calls per day. What is the probability that there will be more emergency calls than they can handle on a given day? (Your answer should include specifically stating what distribution, including parameter/s you are using to calculate the probability) [12 marks] 6. The scheduling manager for an electricity supply company knows that there are on average 12 emergency calls regarding power failures per month. Assume that the number of emergency calls per month can be modelled by a Poisson process and that there are 30 days in every month. (a) What is the probability that the company receives no emergency calls in a particular month? (b) What is the probability that at least 3 emergency calls in a particular month? (c) What is the expected number of emergency calls in a particular month? What is the variance? (d) Suppose that the company can handle a maximum of two emergency calls per day. What is the probability that there will be more emergency calls than they can handle on a given day? (Your answer should include specifically stating what distribution, including parameter/s you are using to calculate the probability) [12 marks]

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