00:01
All right, so we're told customers arrive randomly at a department store at an average rate of 2 .8 per minute.
00:06
I'm going to call that per 60 seconds.
00:09
And we're going to ask some questions about the arrival of customers, assuming that they arrive at a poison, using a poison distribution.
00:21
So the first question asks us to calculate the probability that no customers arrive.
00:26
So basically the probability that x is equal to zero.
00:29
All right, so before i do that, let's get into what the poison distribution is.
00:34
So it's going to be p of x equals e to the negative lambda times lambda to the x all over x quantity factorial, or x factorial.
00:46
And so when x is zero, what we do is we substitute zero in for the function here.
00:51
And lambda is this value right here.
00:53
And this is for one minute or 60 seconds, 2 .8.
00:57
So our function is negative 2 .8 here.
01:00
And then here is a printout for my spreadsheet where x is 0 1 2 and 3 so you substitute 0 1 2 or 3 of this formula you get these probabilities so the probability that x is 0 there are no customers arriving in any particular minute is this 0 .06 6 we'll go to 3 decimals we'll go to 0 .06 1 right and then question 2 asks us for the probability that exactly 3 well look in our spreadsheet when x is 3 it's this 0 .222 .0 .2 .2 .2.
01:48
Question 3 asks us the probability that 3 or more, so that x is greater than or equal to 3.
01:57
So now the poison distribution is discrete.
02:00
So what that means is we want three or more, but there's an infinite number of xes that we, or x can be infinite, zero to infinity.
02:09
So we can't really do that.
02:10
So we're going to do a little complementary event here.
02:15
So the complement of x greater than equal to three, well, that's going to be the probability that x is strictly less than three.
02:23
So that means it's going to be the sum of the 0, 1, and 2 probability that's that.
02:28
But the way we get three or more is we do 1 minus that value...