Final answer:
The statement about the normal curve table is true, as it provides the probability for areas between the mean and a z-score, as well as the tails for any given z-score in a standard normal distribution.
Step-by-step explanation:
The statement regarding the normal curve table is true. This table, often referred to as the z-table, provides the percentage or probability (expressed as an area under the curve) between the mean (μ) of a standard normal distribution and a particular z-score, as well as the percentages in the tails for any z-score. The probability that a score falls within a certain range can be determined by calculating the z-score, which indicates how many standard deviations a value is from the mean. With this z-score, you can then reference a z-table to find the area to the left of the z-score, which represents the cumulative probability up to that point.
The process involves locating your calculated z-score in the z-table. If you want to find the area to the right, you can subtract this value from 1 (the total area under the curve, since it represents the entire population). For example, if you need to know the percentage of scores that lie between two z-scores, you would locate the areas corresponding to both z-scores and take the difference between them. The z-table also enables us to apply the empirical rule (the 68-95-99.7 rule), which states that approximately 68% of observed values lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations in a normal distribution.