Final answer:
The proportion of a standard normal distribution that lies between z scores of -1.96 and 1.96 is approximately 95%, according to the empirical rule or the 68-95-99.7 rule.
Step-by-step explanation:
The proportion of the curve that falls between the z scores of -1.96 and 1.96 is approximately 95%. This is due to the properties of the standard normal distribution, as described by the empirical rule, also known as the 68-95-99.7 rule. In a standard normal distribution, approximately 68% of the values lie between -1 and +1 z scores, 95% between -2 and +2 z scores, and 99.7% between -3 and +3 z scores.
To find the precise value, you look at the normal distribution table for the area to the left of z=1.96, which is 0.475, and then you double it (since the curve is symmetrical) to include the area to the left of z=-1.96, resulting in a total area of 0.95 or 95%.