# Thread: how to get probability from a normal distribution?

1. ## how to get probability from a normal distribution?

If I had Z=Y^3 where Y is a standard normal distribution. How would I approx. calculate the probability of Z<=1 ?, I would understand it if it was Z=Y^2 which is chi-square...

2. ## Re: how to get probability from a normal distribution?

If Z = Y^3 and you want to know P(Z < 1) you can just work with that. You don't actually need to find the distribution of Z.

P(Z < 1) = P(Y^3 < 1) = P(Y < 1) (take some time to convince yourself of that last step). And since you know the distribution of Y you can find that last probability.

3. ## Re: how to get probability from a normal distribution?

i got the probability of Y<=1 is just 0.84134, is that right?
So how would the graphs look, of Y^1, Y^2, Y^3....

ALSO
does cubing the standard normal distribution, make the deviation higher and variance smaller?

4. ## Re: how to get probability from a normal distribution?

Originally Posted by omega
i got the probability of Y<=1 is just 0.84134, is that right?
Looks fine to me.
So how would the graphs look, of Y^1, Y^2, Y^3....
Are you talking about graphs of the pdfs?

5. ## Re: how to get probability from a normal distribution?

ok thanks, yeah i just wanted to know what a cubed standard normal dist. would look like (pdf graph).

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