How to get probability from a normal distribution?

[sneaky666]

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...

 

[mathman]

P(Z ≤ 1)=P(Y ≤ 1). In general for odd powers, you just need to take the appropriate root of the constant of interest.

 

[sneaky666]

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 pdf graph look for Y^3 ?

 

[mathman]

I assume you meant X^3 = Y. Plot pdf for normal distribution. Change X coordinates to Y^(1/3) and replot to be linear in Y.