00:01
For this problem, we know that the number of loaves of bread sold follows a poisson distribution with a parameter lambda equals 5 per hour.
00:17
So that means that the probability that we sell k loaves of bread in a particular hour is going to be given by, well it's generally speaking, lambda to the power of k times e to the power of negative lambda divided by k factorial.
00:29
Or in this specific case, well that's 5 to the power of k times e to the power of negative 5 divided by k factorial.
00:37
For part a, to find the probability that the bakery sells exactly 3 loaves of bread, that's going to be 5 to the power of 3 times e to the power of negative 5 divided by 3 factorial, so that's 3 times 2 times 1, which gives us a result of 0 .1404.
00:59
For part b, to find the probability that the bakery sells more than 6 loaves in an hour, probability of x greater than, strictly greater than 6, we can take 1 minus the sum from k equals 0 up to 5, so that's 1 minus probability that k is, or pardon me, 1 minus probability that x is less than or equal to 5.
01:22
And take the sum from k equals 0 up to 5 of probability x equals k.
01:26
So what i'll do for that is i'll use a little bit of a trick in my software.
01:32
So i'll say create a table where i'll, what i'll do is use my software to generate the list of the probabilities.
01:40
So i say i want a table for k between 0 and 5, just so that you can see if you're working through the numbers with a calculator or something along those lines, then you can confirm that you're getting the right results.
01:50
But i'm just applying this general probability x equals k formula, just plugging in the different values of k...