Final answer:
The probability that a z-score falls between -1 and 1 in a standard normal distribution is approximately 0.68, according to the empirical rule (68-95-99.7 rule) and verifiable through a z-table.
Step-by-step explanation:
For a standard normal distribution, the question seeks to identify the probability that the z-score falls between -1 and 1, which is represented as P ( -1 < z < 1 ). The correct answer is A) 0.68, as this range captures approximately 68% of the area under a standard normal curve, according to the empirical rule commonly known as the 68-95-99.7 rule.
This rule states that about 68 percent of values lie within one standard deviation (which corresponds to z-scores of -1 and 1), about 95 percent of values lie within two standard deviations (z-scores of -2 and 2), and about 99.7 percent lie within three standard deviations (z-scores of -3 and 3) from the mean in a normal distribution. This fact can be verified using a z-table which shows the area to the left of a z-score, or through the use of statistical software or a calculator capable of providing probabilities for a standard normal distribution.