So I was wondering with the bell curve stuff...and all the ways you can solve a question {binompdf/cdf, normalcdf, invNorm} I was wondering what the difference between binomial distribution and normal distribution is and how can I know which method to use without confusing binomial and normal/invNorm? Does norm. distributon always mean that the mean is 0 and standard deviation is 1? o_o
Okay, so a bell curve is a normal distribution, as the stats are normally distributed along the bell curve - and a cross section of said bell curve will provide a normal, logical number that can be related to Z, whereas random cannot. Binomial distribution is where the stats are distributed randomly. Binompdf relates to either having one or the other. eg. either going somewhere, or not going somewhere - and this can be expressed as X~Bi(n , p), where n is the number of tries, and p is the probability of a 'success'. There is also q, which is 1 minus p, which is obviously the probability of a failure. Binompdf, in a calculator, can be used as binompdf(n,p,x), where x is the number you want the probability of appearing. Alternatively, you can do it via nCr(n,x)*p^x*q^(n-x). If my random jarble there makes any sense These are typically questions that ask something like: Sally goes to the shop everyday. Her shopping is randomly distributed in terms of the amount of oranges she buys. The probability that she buys x oranges is shown in the following probability distribution table. Or something like that. Okay, now for normals. Bell curves and the like. In these questions, you're given the standard deviation, and the mean. Or you're given something like 4% are over a given value, and 4% are under, and you're able to assume the mean from this. Two types of questions: Z questions and standard questions. Standard questions will give you: mean and standard deviation. Then it will ask you something like: Where do 97.5% of the values lie? Where do 34% of the values lie? Pr(X<x<Z)? Etc. Z questions make you apply the Z distribution to the question. So this is where invNorm comes into play. Assuming you have knowledge of how Z works, and the invNorm function, you draw the two bell curves. So X is the curve that relates to the question, Z is under it. To use the example from before, X has 4% over a given value, and 4% under a given value - X1 and X2. Z also has 4% over a given value, and 4% under a given value - Z1 and Z2. Then you put this into invNorm to find Z1 and Z2, and make simultaneous equations from the theory that Z = (mean - X)/Standard deviation. So in that you pretty much use X1 and Z1 and X2 and Z2 in the respective equations and either solve them in the calculator or by hand. Hope that helped
Pretty much what Will said. Binomial = discrete, so you'll get a probability mass function that looks something like: If you learned about Bernoulli distributions, it's just that, but a sequence of them. So a Bernoulli would be one flip of the coin (only two outcomes), while a Binomial would be when you flip the coin more than once. So just remember, if there's only two outcomes, use Binomial or Bernoulli. Normal = Continuous. You know what a bell curve looks like, but keep in mind that even if a bell curve is positively or negatively skewed, it can still be considered normally distributed. You'll usually give a question where you're given the population sd and usually have to find the sample mean, or other alternatives will mentioned above. If you think about continuous, and you take a sample of heights from all the males in your class, they should be approximately distributed. That is, their mean will be a certain number (say 155cm), which means approx 50% of the males in your class will be above that, and approx 50% under that. In answer to your other question, it's impossible to have a height of 0cm right? Even more so with a negative height. So a normal distribution doesn't always mean that a mean is 0, nor a sd of 1. It depends on the sample/population and the situation. Rarely you'll have it as exactly 1 in real life.