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View Full Version : Standard Normal Probability Question - BASIC?


breepi
Mar 3, 2012, 08:01 PM
This is a really basic question about a rule... I missed my lecture as I was studying for an exam, and was hoping that someone could shed some light on this for me.

(I'm making up symbols - <= is being 'less than or equal to')

I understand that probabilities have to be represented in a P(Z<= z) - but it looks as if you can assume that if P(Z<z) then P(Z<=z) - am I reading this right?

Thanks so much!

ebaines
Mar 5, 2012, 12:33 PM
it looks as if you can assume that if P(Z<z) then P(Z<=z) - am I reading this right?

Yes - the cumulative distribution function is continuous, so the values provided in the tables is for the probability that z is less than or equal to the value you are looking up. Mathematically the values are the area under the normal dstribution curve between x=0 and x=z:

\displaystyle \Phi (z) = \frac 1 {\sqrt{2 \pi}} \int_0 ^z e^{\frac {x^2} 2}dx