The time (in minutes) between arrivals of customers to a...

The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.56. Part a) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part c) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?

Transcript

00:01 Hi, i'm david and i'm here to help you asking your question.

00:03 Now let me bring up your question here.

00:06 In the question here, we want to reveal about the exponential distribution.

00:10 Let me remind you that if we have the x that followed by exponential, when the mean equal to the peta, and then the density of the x, it will equal to the 1 over peta, and then e to the power minus x over peta, and for the x greater than 0, and also the cumulative distribution function, f capital, on the x, it would equal to probability the x smaller equal to the small x, equal to 1 minus e to the pound minus x over beta.

00:44 Another probability about exponential, it could be memory list.

00:51 So it means that the probability of the x greater than the t, given then the x or equated than the s, it just equal to the probability of the x greater than the t, which is equal to the probability minus s.

01:05 And now in this question here, we've given that the time x, it will follow by exponential, with the mean equal to the 0 .56.

01:18 Now therefore, we should be able to write down the density under x, it will equal to 1 over 0 .56, e to the power minus x over 0 .56 for the x greater than 0.

01:30 Also the cumulative distribution function, 1 minus e to the power, minus x over 0 .56 for the x greater than 0.

01:39 And the question i ask me that you find the probability that the time between the consecutive customers is less than 15.

01:47 So x can be smaller than the 15 seconds.

01:50 So it means that it's equal to the f capital of the 15 and it will apply into this formula here we get equal to 1 minus e to the power of the minus 5.

02:04 15 dividing by, or this one will be in the minute.

02:10 So therefore we need to convert the 15 into the minute.

02:13 So we have to be careful about the unit here.

02:18 15 second, convert into the minute, it will equal to the 15, we divide by 60, equal to the 0 .25.

02:30 So therefore we get equal to the probability of, it will equal to the f capital of the 0 .25 equal to 1 minus the e to the power minus 0 .25 divided by 0 .56.

02:49 And if we compute it, we have 0 .25 0 .25 to 0 .56, each the power of the minus answer.

02:59 1 minus that equal to the 0 .36.

03:03 I want to round the answer into the 4 decimal places...

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