Welcome back, guys. Your lean six sigma green though Uncaf three Mukai over and today we're going to continue distributions and talk about the binomial distribution.
So you're binomial distributions. Not as sexy as you are. Normal distributions. But it's important for you to know this is a green belt because this is one of our discrete data distributions and something that you will probably run into through your course of analyzing data.
So from this module, I want you to be able to understand and recognize the binomial distribution.
And I want you to understand the conditions for ah binomial distribution.
So by no meal, the body gives you kind of a hint as to what it means. This is going to be your to response data. Yes. No positive. Negative. So if you think back to when we were divided, we were designing our data collection plan and we thought about my room service and we looked at it two ways, we looked at it
continuous, where it took us
21 minutes and 15 seconds to deliver. And we also looked at a discreet. Did we deliver within the time frame or didn't we?
This is going to be the yes, no part of it. A couple of other things that you need fixed number of trials.
So you need to know what your population, which is also generally your sample and a binomial, is. You also meet to know your probability. So what is the likelihood of a positive on an easy way to mathematically derived
If you have a buying no meal distribution
is that your mean is greater than your variants? Remember, your variants is part of your standard deviation, so you'll look at your average variance. If your mean is larger than that, you will most likely be working with a binomial distribution. So you may ask yourself,
How do I get my probability?
This is going to be one of your historical distributions, unless you are, of course, flipping a coin, which is how we're trained on binomial distributions. So on the left you are looking at a binomial distribution with 10 trials so 10 down at samples
and a probability of 50%.
So what this tells us is what is the likelihood so p of X that we're going to get each one of these measures? So
what is the likelihood that we will get three positives and seven negatives. What's the likelihood that we will get five positives and five negatives? This is, of course, we're flipping a coin, and we know that we have a 50% likelihood positive or negative.
If you look at your positive negative data and it looks more like the data on the right,
then this means that we need to do an intervention because we having negative skew. So the majority of our data is on the negative side. Are probability is point to, unless we want a negative skew, which, in that case, yeah, we are meeting our goal.
But so important things from the binomial distribution.
What is the likelihood that we're going to get the result that we want based off of number of trials on and generally your baseline or your starting point is 50 50? As you get better at delivering your room service,
your probability will change. So if for some reason,
let's say that I want to do, I'm looking at the right. So we have 10 trials on, and I want to know what is the likelihood that all 10 of them will give me two successes. I will read this and I will see the probability is 30%.
If I then run those trials on and I get 100 successes. We know that there is variation. We're gonna call it special cause. But what that means is there is something on the exterior working on this process. If we're delivering room service,
my first instinct would say there is something wrong with the timekeeping device.
So let's do an additional M s A or gauge R and R and let's re validate our measurement system.
But so binomial distributions Not really that used because it is discrete data, so we tend to look at it in other ways. But if you need to the probability and the distribution, you're gonna want to do it by no meal. You understand that you must know the number of trials.
Ideally, you know the probability because you can then graph it.
But if you don't, you must know the number of trials. This must be a to response only and
oh, and mean, mean is larger than variance. So if you were to calculate this mathematically, you would see that you're mean is larger than your variant. That's how you're going to know that this is a binomial distribution.
All right, guys, next one up, our last greenbelt distribution, we're gonna talk about the police son distribution.