SAT verbal scores are normally distributed with a mean of 450 and a standard deviation of 120. Determine the percentage of scores falling between 450 and 570.

To determine the percentage of scores that fall between 450 and 570 on the SAT verbal section, which is normally distributed with a mean (μ) of 450 and a standard deviation (σ) of 120, we will use the standard normal distribution (Z- scores).

First, we need to convert the raw scores to Z-scores. The formula to calculate the Z-score for a value X is:

Z = (X - μ) / σ

Let's calculate the Z-scores for 450 and 570:

For X = 450 (which is the mean): Z_450 = (450 - 450) / 120 = 0

For X = 570: Z_570 = (570 - 450) / 120 = 120 / 120 = 1

Now, we want to find the area under the normal distribution curve between Z = 0 and Z = 1. This area represents the percentage of scores between 450 and 570.

We can use a standard normal distribution table, a calculator, or statistical software to find the area to the left of Z = 1. Typically, this value corresponds to a percentage (or probability) of 0.8413 or 84.13%.

Since a Z-score of 0 corresponds to the mean (which is 50th percentile), the percentage of scores between the mean and a Z-score of 1 is:

84.13% - 50% = 34.13%

Thus, approximately 34.13% of scores fall between 450 and 570 on the SAT verbal section.