Incoming phone calls generally are thought to be poisson...

Incoming phone calls generally are thought to be Poisson distributed. Assuming an operator averages 2.2 phone calls every 30 seconds. a) What is the expected amount of time between calls? [5 marks] b) What is the probability that less than one minute would elapse between incoming calls? [5 marks] c) If the operator needs to talk to her supervisor for 2 minutes, what is the probability that the operator will not miss any incoming call when she finishes talking to her supervisor? [5 marks]

Transcript

00:01 Once again, welcome to a new problem.

00:05 This time we're dealing with probabilities.

00:08 We're dealing with probability.

00:10 And when it comes to probability, we have an understanding that this has to do with quantification.

00:20 Quantification of chance processes.

00:25 So you're quantifying chance processes.

00:27 So, for example, probability of heads is one half.

00:32 And probability of tails is also one half.

00:36 These are equally likely events.

00:44 These are equally likely events.

00:47 And there's a special type of probability distribution.

00:54 There's a special type of probability distribution called the poison probability distribution.

01:01 And this one is, determines how many times how many times an event is likely to occur of a specified, of a specified period.

01:34 So the likelihood of an event happening over a specified period.

01:42 And typically when it comes to a poison distribution, we have these special formulas for the type of poison probability distribution.

01:56 We have a new problem and in this particular problem, we looking at the fact that we're looking at incoming phone calls and we're looking at incoming phone calls and the distribution is poison with an average of 2 .2 phone calls phone calls every 30 seconds, every 30 seconds.

02:36 So the first thing we're going to do is determine the expected time between calls.

02:51 So we want to determine the expected times.

02:57 So if we're having 2 .2 phone calls every 30 seconds, this is a poison distribution.

03:08 So the operator averages would be 2 .2 per 30 calls per second.

03:22 And so the amount of time between calls has a mean of mean of one of a lambda, you know, exponential distribution...

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