Question

the standard normal curve shown below models the population distribution of a random variable. What proportion of the values in the population does not lie between the two z-scores indicated on the diagram

Answer 1

we'd need to see the z-scores and the diagram to answer this fully

that being said - each z-score corresponds to an area on the curve to the left of the z-score. if the z-scores are the integers -3 to 3 you can use the empirical rule (I'll attach a diagram below).

if not, you'll have to convert the z-scores to percentiles and subtract the two percentiles to find the area between them, then 1 - that area to find the area *not* between the two z-scores.