 This is an example on how to find usual and unusual values of a binomial experiment or binomial distribution. A certain species of dragons lays eggs that are green or yellow. It has been observed that 22% of the eggs are yellow and the rest green. Next spring, a scientist has been given permission to randomly select 47 of the dragon eggs to incubate. What is the minimum usual number of yellow eggs? What is the maximum number of yellow eggs? This is a binomial experiment because he has 47 trials. And since we're talking about yellow eggs, the probability of a success of choosing a yellow egg, each trial would be 22%. So let's write our parameters down over here on the right-hand side. 47 trials, probability of a success, meaning we pick out a yellow egg. Yellow egg is considered a success. And Q is always 1 minus P or 1 minus 0.22, which gives you 0.78. So the general range rule of thumb says that minimum usual value would be your mean minus two standard deviations. So first we need to find the mean of this binomial distribution, mu. It's n times P. It's 47 times 0.22. 47 times 0.22. That is going to give you 10.34. It would be wise likely to round this to 10, but I'm going to keep this exact answer. So that way I don't have rounding errors when I find the minimum and the maximum usual values here. Standard deviation is square root times n times P times Q, a square root of 47 times 0.22 times 0.78. It gives you square root of 8.0652, which is 2.84. That is my standard deviation. Now the more decimal places you keep, the more accurate your answer is going to be as I find the minimum maximum number of usual values. So if you want to, you can go out more decimal places in just two. Alright, so mu minus 2 sigma, minimum usual number of yellow eggs. I have 10.34 minus 2 times 2.84. Plug that into your calculator and you get 4.66. And you will always round up your minimum usual value. Always round up. Because if I was to get 4, that would be much lower than the minimum usual value here. So 5. 5 is the minimum usual number. Now as a warning here, it is possible sometimes for you to get a negative number for your minimum usual value. In the instance you get a negative number, such as in this case, you can't have a negative number of dragon eggs. So you automatically just by default make the minimum usual number zero. But once again, if you ever get a negative minimum usual number, you will typically use zero as the minimum usual number because you can't have negative with something. Alright, next, maximum number of yellow eggs, minimum usual number of yellow eggs. Alright, so maximum usual number. I have 10.34 plus 2 times 2.84. I believe that's going to give you 16.02. And maximum number you always round down, regardless. If this was 16.75, I would still round down to 16. So 16 is maximum usual number. As I said, usual number of yellow eggs would be between 5 and 16.