Normal probability

Question

I have a very simple question. What is the basis of normal probability, i.e. What are the probabilities? I am testing the standard normal distribution. My normplot (in MATLAB) showed that the values ​​were more or less in a straight line, but the probability of 0.5 corresponded to a value other than zero.

My question is how do I interpret this? Does this mean that my data is usually distributed, but has a non-zero average (that is, not a standard normal) or does this probability reflect only something else? I tried Google, and one link said that probabilities are cumulative probabilities from the z-table, and I cannot figure out what to do with it.

Also, does MATLAB exist that, as long as the values ​​are adjusted to the line drawn by the program (red dashed line), the values ​​come from the normal distribution? In one of my graphs, the dashed line is very steep, but the values ​​fit in, does this mean that one or two values ​​that are outside this line are just outliers?

I am very new to statistics, so please help!

Thanks!

Answer 1

My question is how do I interpret this? Does this mean that my data is usually distributed, but has a non-zero average (that is, not a standard normal) or does this probability reflect only something?

You're right. If you run normplot and get the data very close to the set line, it means that your data has a cumulative distribution function , which is very close to the normal distribution, Point 0.5 CDF corresponds to the average value of the set normal distribution. (It looks like 0.002 in your case)

The reason you get a straight line is because the y axis is non-linear, and it is made “deformed” so that the ideal Gaussian cumulative distribution will map into a line: the signs of the y axis are linear with the inverse function.

When you look at the ends and they have steeper slopes than the corresponding line, this means that your distribution has shorter tails than the normal distribution, i.e. there are fewer outliers, possibly due to some physical restriction that prevents excessive deviation from average.

Answer 2

Normal distribution is a function of density. The probability of any single value will be 0. This is because you have the total probability (= 1) distributed between an infinite number of values ​​(its continuous function).

What you have on the graph (normal distribution) is how the probability (y axis) is distributed around the values ​​(x axis). So what you can get from the graph is the probability of an interval between two points, from -infinite to any point or from any point to + infinte. This probability is obtained by integrating a function (normal distribution) determined from point 1 to point 2.

But you do not need to do this integral, since you have a table z. Table z gives you the probability that x is between -infinite and x (approaching the equation that relates x to z)

I don't have MATLAB here, but I think the straight line you are talking about is a cumulative distribution function that tells you the probability of x between [-infinite, x] and is determined by the sum (or integral in this case) from -infinite to x value (or obtained in table z)

Sorry if my english was bad. Hope I have been helpful.