# 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. Originally Posted by Sneaky
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...
My first thought is that you should be able to calculate the pdf of Y^3 using one of the techniques you would have been taught. Then integrate it using a numerical technique (or a CAS).

3. well i have to do P(Y<=1) = P(X^3<=1) = P(X<=1), and since X ~N(0,1), so I can just look in the book for the standard normal distribution values
which is just 0.84134, is that right?
By the way out of curiosity how would the graph look for Y^3 ?

4. Originally Posted by Sneaky
well i have to do P(Y<=1) = P(X^3<=1) = P(X<=1), and since X ~N(0,1), so I can just look in the book for the standard normal distribution values
which is just 0.84134, is that right?
By the way out of curiosity how would the graph look for Y^3 ?