00:01
Hey there, welcome to numerade.
00:03
We are asked to find a probability that a customer would have to wait between 45 and 15 seconds, where we're given our average customer waiting time as 20 seconds.
00:16
So we can denote our average here as lambda, so lambda equals 20, and as you might know, this will follow a pusan distribution because we're given our average here, and we're asked to find our probability.
00:32
So our person distribution formula is basically the probability of x equals our constant e raised to negative lambda, multiplied by lambda raised to the x.
00:44
This is then divided by x factorial.
00:48
So knowing this here, we're going to start with part a.
00:54
So for part a, find a probability that a customer would have to wait between 15 and 45.
01:01
Seconds.
01:02
So the probability that x is between 15 and 45.
01:12
Let's assume that they are inclusive.
01:17
This is basically proportional to x being less than or equal to 45 minus the probability that x is less than 15.
01:27
Knowing this here we can plug in our probabilities into our equation above given us so let's see what we get here so we have 45 seconds let's see what we get here lambda equals 20 and 45 all right so what we get here is basically very close to 1 so 1 .000 0000 minus the probability the x is less than 15 so we have 15 giving us a value of around.
02:19
So this one will be 0 .1049...