00:01
Hi, i'm david and i'm here to have you answer your question.
00:04
Now let me bring up your question here.
00:07
In the question we'll discuss about the exponential distribution.
00:10
Let me remind you that if we have the x followed by the exponential with the mean equal to beta and then the density of the x equal to one number beta, each the power minus x over the peta for the x greater than 0.
00:32
In this question here we're given the x, it will be the amount of time spent on the bank.
00:38
So that will be the time followed by exponential.
00:42
That will be the mean beta equal to the 10 minutes.
00:47
Therefore, the density of the x, it will equal to 1 over 10, each the power minus x over 10, but the x greater than 0.
00:57
Now we will have mean 10 minutes that is mule under.
01:05
So let me see exponential distribution will do mean 10 minutes.
01:10
That is one out of 15.
01:15
So let me see it will be this one will be one over 15.
01:25
I'm not sure about this notation here but let's move it on now and x will be in minute.
01:35
And now in the part i am the question.
01:39
What is a probability that the customer will spend more than 25 minutes in the bank.
01:44
So you want to find the probability that x would be greater than the 25 minutes.
01:53
And this one just equal to the integral from 25 up to infinity, 1 over 10, e to the power minus x over 10 the x.
02:06
Now this integral, it will equal to anti -derivative will be minus e to the bar minus x over 10 evaluate from 25 to infinity.
02:17
If we put the infinity inside, we got the 0.
02:21
If we put the 25 inside, we have the e power minus 25 over 10...