00:01
In this question, we are told that the arrival of customers follows a poisson distribution.
00:07
And for part a, it's given that they arrive at a rate of four every five minutes.
00:13
So what is the probability that more than four customers arrive in a five minute period? so let's let x be the number of customers that arrive in a five minute period.
00:38
Now the probability mass function for a poisson random variable is given by this form.
00:47
This formula.
00:52
So lambda to the exponent x times e to the minus lambda over x factorial.
01:03
And we want the probability that x is greater than 4.
01:10
This is equal to 1 minus the probability that x is at most 4.
01:18
And this is equal to 1 minus this summation using the probability mass function.
01:25
We want the summation from x equals 0 up to 4 of the probability mass function.
01:42
Now we can calculate this by hand, it's not too bad.
01:45
There's going to be four terms here.
01:48
Or we can use software.
01:49
So let's use excel...