Question

What are some characteristics of a normal distribution? What does the empirical rule tell you about data spread around the mean? How can this information be used in quality control?

Can you compare apples and oranges, or maybe elephants and butterflies? In most cases the answer is no – unless you first standardize your measurements. What are a standard normal distribution and a standard z score?

Answer 1

Normal distributions are based on random variables whose range is whole real line i.e., the random variable having normal distribution can have negative as well as positive values. This distribution is used in almost all situations also by the large sample property any data which has a large number of observations have a high probability of having normal distribution. The normal distribution is unimodal, symmetric i.e., mean=median=mode. this property makes it even more useful in real situations. The area under the curve property indicates that for 3*sigma limits almost 99 % data will lie under this distribution. The standard normal distribution (SND) is normalization of any random variable which has large data or which follows normal distribution. Also, calculating probabilities under SND distribution becomes very easy as Z-score table is available for the calculation of the probability of any random variable. There are usually two types of z-tables one is where we get the area (probability) from

-infinity to z and one is where area is given from 0 to z. The SND is symmetric about 0 i.e., 1/2 probability exists left of 0 and 1/2 exists on the right side of 0.