00:01
In this question we are told that the number of eggs that a chicken lays follows a poisson distribution with an average rate of 4 per hour.
00:13
And for part we want the probability that exactly 3 eggs are laid in the next hour.
00:24
So let's identify the probability function for a poisson random variable.
00:49
So for x equals 3, using the probability function we have the following.
00:54
Following.
01:11
And we get a probability of approximately 0 .1954.
01:23
For part b we want the probability of 2 eggs in the next half hour.
01:28
So here the duration is half an hour.
01:32
We want the probability that x is equal to 2.
01:52
And this comes out to 0 .2707.
02:04
For c we want the probability of fewer than 3 eggs in a 4 hour shift.
02:10
So here is 4 hours.
02:13
And we want the probability of fewer fewer than 3 eggs.
02:21
So as a cumulative probability, this is the probability of at most 2 eggs.
02:29
Let's solve this using excel...