Final answer:
Approximately 68.3% of standardized test scores fall between 401 and 639. Approximately 31.7% of standardized test scores are less than 401 or greater than 639. Approximately 2.3% of standardized test scores are greater than 758.
Step-by-step explanation:
To find the percentage of standardized test scores between 401 and 639, we need to find the area under the bell curve between these two values. First, we need to standardize the values using z-scores. The z-score for 401 is (401 - 520) / 119 = -0.999, and the z-score for 639 is (639 - 520) / 119 = 0.999. Then, we can use a standard normal distribution table or a calculator to find the area between these two z-scores. The area is approximately 0.6826, which means that approximately 68.3% of standardized test scores fall between 401 and 639.
To find the percentage of standardized test scores less than 401 or greater than 639, we can calculate the area to the left of 401 and the area to the right of 639 using the standard normal distribution table or a calculator. The area to the left of -0.999 is approximately 0.1587, and the area to the right of 0.999 is also approximately 0.1587. Therefore, the percentage of standardized test scores less than 401 or greater than 639 is approximately 0.1587 + 0.1587 = 0.3174, which is equivalent to 31.7%.
To find the percentage of standardized test scores greater than 758, we need to first find the z-score for 758, which is (758 - 520) / 119 = 1.999. Then, we can calculate the area to the right of 1.999 using the standard normal distribution table or a calculator. The area is approximately 0.0228, which means that approximately 2.3% of standardized test scores are greater than 758.