Why do we need to do this? If you remember our work with the Binomial Distribution you remember that there was a table for every value of n (sample size) with rows (x values) and columns (p values - probabilities) for a range of values of n, x and p. With the use of a z Score we will be able to transform any normal probability distribution into a "Standard Normal Distribution.". To determine a probability we will start with a z Score which is calculated as z = (X - Mean)/Standard Deviation. In our case one of the values will always be the mean of the probability distribution. When dealing with with continuous distributions, and in our case it will usually be the normal distribution (pictured below) we will talk about the probability that x will be between certain values.įor continuous distributions the probability that the variable will fall between two values is the area under the curve between those values. Thus when we discussed the Empirical Rule we talked about 68% of the data being between the mean plus one standard deviation and the mean minus one standard deviation (mean +s and mean-s). In continuous probability distributions we can't point to specific values of x with spaces between the x values. ![]() The Concept - When we were dealing with discrete probability distributions each value of x was related to a specific probability.
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