0:00
Hello.
00:02
So let's first look at what the information we got.
00:05
So we got the average number of customers.
00:14
Okay, per hour.
00:18
That is 10.
00:20
So the expected number, let's a second.
00:28
The expected number of customers in 20 minutes.
00:39
Customers in 20 minutes, that should be 10 times 20 over 60.
00:53
We're going to be 10 divided by 3 so this is 20 over 60 we're converting the minutes to hours okay so we divide by 60 okay so that's the expected number of customers in 20 minutes so once we have that we cannot answer the first part of the question which is the probability that a customer will come within 20 minutes of opening.
01:46
What is that? that is you go to 1 minus the probability of no customer.
01:55
So let's first find the probability of no customer.
02:00
So this is a poucazone distribution which is given by e to the negative lambda times lambda to the x divided by x factorial.
02:18
So no customer x is 0 and then negative lambda is the expectation.
02:27
So that's 10 over the expectation of the mean if you like times 10 divided by 3 as 0 over 0 factorial.
02:41
This is just e to the negative 10 over 3.
02:45
Oops.
02:50
That's going to give 0 .0357.
03:00
So now we can see that the probability that a customer will come in within 20 minutes...