Final answer:
To find the percentages of standardized test scores within certain ranges, we need to calculate the corresponding z-scores and use the standard normal distribution table. The percentage between 420 and 630 is approximately 68%. The percentage less than 420 is approximately 15.87%, and the percentage greater than 735 is approximately 2.28%.
Step-by-step explanation:
To find the percentage of standardized test scores between 420 and 630, we need to calculate the z-scores for these values and then use the standard normal distribution table to find the corresponding percentages.
(a) Z-score for 420 = (420 - 525) / 105 = -1.0. Z-score for 630 = (630 - 525) / 105 = 1.0. From the standard normal distribution table, we can find that the percentage between -1.0 and 1.0 is approximately 68%.
(b) Z-score for 420 = -1.0. From the standard normal distribution table, we can find that the percentage below -1.0 is approximately 15.87%. Therefore, the percentage of standardized test scores less than 420 is approximately 15.87%.
(c) Z-score for 735 = (735 - 525) / 105 = 2.0. From the standard normal distribution table, we can find that the percentage above 2.0 is approximately 2.28%. Therefore, the percentage of standardized test scores greater than 735 is approximately 2.28%.