How come probability of a normal distribution can be greater than 1?

Question

So I have a normal distribution with the mean 4.8 and standard deviation 0.3

When I calculate the probability of X let say X = 4.59

I get the result = 1.0408 (using Excel =NORMDIST function)

Why is that?

How can it be greater than 1?

Answer 1

It is probably because you are considering the density function of the normal distribution... The density may well be quite high near the mean value - especially if the deviation is relatively low. This is because many outcomes will lie close to each other in this range so the outcomes have a high density in this range. This is not to be confused with the probability!



For a continuous stochastic variable the probability of a specific outcome is always equal to 0 whereas the probability for an interval will be positive.



Such a positive probability corresponds to the area under the graph of the density function. The entire area under the entire graph of the density function should be 1! This can also be true regardles of some function values being greater than 1.

Answer 2

It can't... so let's have a look.



I'm guessing you entered the formula "=NORMDIST(4.59,4.8,0.3,FALSE)" which gave me the same value. By entering "false" you're telling excel to find the height of the curve at that value (probability mass function).



If you switch it to true you are instead telling it to use a cumulative density formula, and it will tell you the probability that the value is less than x. If you care to confirm, I got .242

Answer 3

you're able to opt to calculate the z-center of the fee first, it somewhat is given by way of skill of z = ( 12 - ? ) / ? From there you may desire to the two seek for for the possibility linked with that z-score in undemanding statistical tables or use a typical equation to calculate the possibility. many situations you would be looking up in tables while you're purely now gaining expertise of approximately this; the formula is a sprint too complicated.