For example, if you have heights from a population with µ = 63.5 and σ=2.80, and you want to find the probability that a randomly selected person has a height of less than 70.0 inches (so, we are working in decimal inches). You get z = (X-µ)/σ = (70.0-63.5)/2.80 = 2.32142857143.

If you are using a table, you are forced to either:

(1) look up 2.32 in a table to get a probability of 0.98983

(2) interpolate using the table, which I am not going to bother doing because the answer wouldn't be as accurate as . . .

(3) use a computer command in some stat software to get an answer like pnorm(2.32142857143) = 0.9898681.

Here's the question: If I am being careful about significant digits, should I report my final answer as 0.990 (three significant digits) because that's how many the z-value I was looking up had (I didn't round the 2.32142857143 because we aren't supposed to round intermediate calculations.)? Or is there some other relationship between z-values and probabilities when it comes to significant figures?