How to deal with Z-score greater than 3?
In a standard normal distribution how do I deal with a $Z$ value greater than 3?
I know that z-score ranges form -3 to 3
Consider this one ...
mean = 70, standard deviation = 4
I need to find $P(65 < X < 85)$.
Transforming to standard normal gives $P(-1.25 < Z < 3.75)$
How to deal with the $3.75$?
Edit *Actually it's not greater than 3, $z < 3.75$. I meant smaller than, sorry. Should I assume it's just 0.4990 or what?
ok i know that but i'm talkin about the standard .. which has table with values from -3 from 3 , i know it's up to infinity but what i want is to find values bigger than 3 which is not listed in the table .. i know there is another exponential formula but it's not for the standard dist.
The $p$-value of $|z|$ statistics that are $\ge 3$ are all *small*. They never get big again... just smaller and smaller. So if your table of $p$-values for $z$ statistics stops at three, it probably says the $p$-value is 0.000 or something like that (really meaning < 0.001), and you can simply use that to conduct your tests.
Let me repeat (and correct) what I've said in my comment ad reply to your edit.
You have to transfer from $X$ to $Z$ in order to use a z-score table. Since a z-score table contains a small finite subset of values, you often must settle for an approximation. So you could also settle for $P(Z<-3)\approx 0$ and $P(Z< 3)\approx 1$ (NB: $P(Z>3)\approx 1$ was a typo, sorry.)
As to $P(-1.25<Z<3.75)$, I'll use this z-score table: $$P(-1.25<Z<3.75)=P(Z<3.75)-P(Z<-1.25)\approx 1-0.1056=0.8944$$