Question

The scholastic assessment test (sat) is standardized to be normally distributed with a mean u = 500 and a standard deviation 0 = 100. What percentage of SAT scores falls between 500 and 600?

Answer 1

To find the percentage of SAT scores between 500 and 600, calculate the z-score for 600 and refer to the normal distribution table. The resulting calculation reveals that 34.13% of SAT scores fall between 500 and 600.

Step-by-step explanation:

The percentage of SAT scores that fall between 500 and 600 can be found using the properties of the normal distribution. The mean (mu) is 500 and the standard deviation (sigma) is 100 for the SAT. To find this percentage, we calculate the z-score for 600. The z-score is given by the formula z = (X - mu) / sigma, where X is the score for which we are finding the z-score. For a score of 600, z = (600 - 500) / 100 = 1. A z-score of 1 corresponds to the 84.13th percentile of a normal distribution, which means that 84.13% of the data lies below this z-score.

Since the mean is also the median in a normal distribution, it implies that 50% of the data lie below a score of 500. Thus, the percentage of scores between 500 and 600 is 84.13% - 50% = 34.13%. Therefore, 34.13% of SAT scores fall between 500 and 600.