00:01
So, for this problem, to begin, i'll note that we are considering independent events, or we're considering the number of independent events in a fixed time interval, where the time interval here is one day, with a constant mean rate.
00:31
So that means that this is going to be appropriate to use a poisson distribution for.
00:45
So x is distributed as a poisson distribution with a mean rate of 14 per day, which means that we have that the probability that x is equal to k will be equal to lambda to the power of k times e to the power of negative lambda divided by k factorial.
01:10
So for part a, we're looking for probability that x is equal to 14.
01:15
So let's see here.
01:18
We have 14, or pardon me, not 14.
01:20
Yes, 14 actually.
01:22
We have 14 to the power of 14 times e to the power of negative 14 divided by 14 factorial.
01:29
So we get a result of 0 .106, roughly.
01:36
Or 0 .1060.
01:38
Then for part b, probability that x is less than or equal to 3, we just take the sum of p of x equals 0, 1, 2, and 3.
01:49
So what i'll do here is put in just k as a placeholder, then i'll substitute in k as 0, 1, 2, and 3.
02:01
So don't worry about the syntax that i'm using here...