Question

In 2015, the college board sat mathematics score of high school seniors, which follow an approximately normal distribution, has a mean of 511 and a standard deviation of 120². What percentage of seniors who took the test in 2015 scored between 271 and 751?

Answer 1

The percentage of seniors who scored between 271 and 751 is approximately 97.49%.

Step-by-step explanation:

To find the percentage of seniors who scored between 271 and 751, we can first convert these scores into z-scores using the formula z = (x - mean) / standard deviation. For the lower score of 271, the z-score would be (271 - 511) / 120 = -2.83. For the higher score of 751, the z-score would be (751 - 511) / 120 = 2.

Next, we can use a z-table or calculator to find the probabilities associated with these z-scores. The probability of a z-score being less than -2.83 is very small, approximately 0.0023. The probability of a z-score being less than 2 is approximately 0.9772.

Therefore, the percentage of seniors who scored between 271 and 751 is approximately (0.9772 - 0.0023) * 100 = 97.49%.