Okay this is stopped and topic number six witches are what distribution to use a means for us this is a discussion about probability distributions are and we're on the up a slab five to see somebody to use/bus to Rio to help page with start at the exam review click on statistics statistics or do we want the PowerPoint presentation to and we will let this opened and we will scroll down to topic top 10 topic number six of the Indian top 10 topic number six is on sly native of should be up to its 80 year so top 10 summers on slide 81. Slide, anyone know what you find that slide again that the name of the the topic is what distribution to use, and I call it a probability distributions on the top 10 topics, and thus the sentences decide what distribution that means what probability distribution binomial nor moral or tea to use in a given situation. And so it sounds difficult, but it isn't really that difficult a binomial distribution by any means to like a bicycle to tires used by normal distribution when he won a compare successes and fail to show anything with two outcomes. Male-female those kinds of things of the normal distribution is the one that you're for an early from earlier at the bell shaped mound curve that we use in the central limit their and the tea distribution is almost just like the all in the normal distribution. It just has kind of longer are fatter tails if you will and the use of in certain cases were weak in or we don't know the population standard deviation, which actually occurs quite often the sole start here and slide 81, which distribution used to use the binomial distribution member biased to luck a bicycle if the random variable is the number of successes in and try off such number of successes or number of failures in and trials that so the first bullet is the random variable is the number of successes in and which means the number of observations sure the number of variables trials trial. This means an independent event each trial is a success or failure to do only two outcomes of like if you flip the point is only two outcomes heads or tails the third bullet says their independent trials we used to call those things were newly trials but after a very famous mathematical family of a independent trials means that will be all of the result that you get on one trial is different than the result that you get on another try the fact that you flipped a coin he got heads once tells you nothing about whether or not, you get tale summits are a number for your constant probability of success called Potter for four or a portion on each trial in the last bullet on slide 82 is sampling with replacement that's generally what we're talking about with of the binomial distribution of that which we take one out of a pile we look at him and we put it back sampling with replacement, but people can use it without sampling without replacement as well okay slight 83 water dichotomous outcomes were the two kinds of outcomes are some examples success versus failure burst all the binomial experiment only result even one of two possible outcomes. Some examples male versus female defective versus non-defect of like in a assembly-line yes or no passed or failed like tougher example to give the eight or more writing answers on an exam or you can by an alcoholic drink or cannot buy alcoholic drink so those are referred to as dichotomous outcomes is only two possible outcomes with a slight 84 remember the binomial distribution is a discrete distribution discrete distribution means that of the values take on integer values as opposed to continue his numbers were, you can always look them in half a double of number to induce an example 012... which means 345678 all way up to an number of observations to my gnome will distribution is often skewed. But in when it's a very large number that can be symmetric as well. And a slight 85, when you use the normal distribution and pay at what is the normal distribution first of all it's a continuous about continuous numbers. Its bell shaped and it's a metric and you know what the bill should looks like is in a per in a perfect in a theoretical normal distribution in other words it if it was perfectly pure data perfectly matched normal distribution in the mean would equal the medium would equal the mode that usually is not the case, but sometimes they can be close particular domain in the media and a number of array of a measurement are some examples and dollars inches and years also add one to this list in units like the number of Coke bottles for example of that should produce an assembly line, things like that of a fourth bullet one of the things that word that's important in the normal distribution is secure and little probability under the normal curve, which usually requires calculates to chart to calculus to calculate correctly, but we usually uses the tables as he and tea tables for that is what we don't want everybody to compute all the difficult work each particular time. So we're what we're interested in is the cumulative probability under the normal Korff base to where you are along the x-axis uses a table. If you know the population mean and the population standard deviation of carrying uses the cable if you know the population mean, and the population standard deviation and then this becomes important later on particularly an hypothesis testing. Usually you will not know the population standard deviation, but the problem will say whether or not, you know her not to pay if it doesn't say you can assume that you don't know. You don't know the population standard deviation pain and the last bullet the sample mean, you can use is a table if you know the population standard deviations which usually will not know but if you use the population standard deviation and you know that the sample came from a normal distribution or the ore that the number of items is greater than 30 day either one of those two on the problem will state that you'll know the hand because I'll be stated in the problem and usually in some kind of word form in the sentence it'll say that the sample was drawn from a normal distribution are normal population or an approximately normal population, those are terms that are quite common and were problems and statistics a slight 86 the tea distribution is also can about continuous revels in its mountain shaped or bell shaped at and isometric and so very similar to the normal distribution, but think of it has it as having wider tales of okay details go off pretty sharp in the normal distribution, and they're a little bit longer little bit wider in the tea distribution of the applications you use the applications to use with the second bullet is the application of the tea distribution is very similar to the application of the normal poster mentioned. It's a little bit more spread out than the normal distribution on and below point number force we use the TV distribution. This is the key issue use a tedious duration of the normal population if it cut that the sample comes from a normal population or approximately normal. You'll be told up the prom, but the population standard deviation is not known, which is usually the case for often takes up a we have to do one additional thing for a tedious tradition have to compute the degrees of freedom at the degrees of freedom is a very simple calculation in the degrees of freedom is equal to 10 minus one so if the number of observations was 32 of freedom is 29 and tank and use steeped in a one for example in this example we're estimating amenable all of one population just degrees of freedom as a number of observations minus one. When you have to compute the degrees of freedom for a tea distribution of pay and last bullet to tea distribution approaches as he do to rich and busy distribution as the number of observations increases or that the number of degrees of freedom increases of kind of the TV distribution starts to look a lot very very close to the Zee distribution as a number of degrees of freedom increases in a demo of one glass slides is the normal is as she is is just remember the key point to use it when you use normal distribution of the tea distribution first bullet use the tea table of tea distribution if if the sample was drawn from an oral population, but the population standard deviation is not known. And in general that's the case, because remember in the population in the values are fixed, but often unknown, because it's hard to its very difficult to see the entire population. So sometimes we can jam we can't, we don't know the population standard deviation in the second bullet is if you're given a sample standard deviation is represented by a lower case us use the tea table assuming the normal population remember there are two neat tables up pieces of paper that you need for the exam so if there's anything you need to look up or know to be given in the problem of paying our eyes. That's the end of the stuff for