Probabilities using Z scores help How to calculate the probability of a z-transformed value does not appear in the table? e. g
What is the probability of randomly drawing a Z-transformed value of 2.465 or greater?
P(Z ≥ 2.46) = 0.0069 & P(Z ≥ 2.47) = 0.0068. it could be any value between 0.0068 and 0.0069???
b) What is P(|Z| ≥ z) = 0.07? it could between -1.81 and 1.81 if we split 0.07?
c)Suppose we have a population with μ=12, σ2=3 and Y~N(12,3).  What is 
P(Y ≥ 9.5)?
d)Suppose you have a population with μ=12, σ2=2 and Y~N(12,2).  What is 
P(Y ≤ -8)? 
 A: It depends whether we are dealing with a real-world question or a graded exercise. 
For an exercise, you can interpolate linearly between $0.0069$ and $0.0068$. Since your point is halfway between $2.46$ and $2.47$, linear interpolation on the tabular values gives $0.00685$. 
The situation is quite different if we are dealing not with gaps between table entries, but with numbers that go beyond the table. For many practical problems, it is enough to say that, for example, $\Pr(Z\gt 4)$ is negligible. But there are situations in which we do need more precise information. There are good formulas available for estimating the probability that $Z\gt z$, where $z$ is medium-sized, say in the range $3$ to $10$.  
Remark: For a real-world application, it's not worth bothering. In a real world problem, we are using the normal distribution as an probabilistic model. Models and the real world are not the same thing. Many probabilistic models fit the real-world only modestly well. (A not very good model can still be useful.) So there is no point to trying for $3$ significant digit accuracy. Anyway, modern software can get you much greater precision than that.  
