Question

students took a college math placement exam with a mean of 200 and a standard deviation of 12. using the empirical rule, approximately, what percent of the students scored above 224?

Answer 1

To find the percentage of students who scored above 224, we can use the empirical rule. Using the z-score formula, we can calculate the z-score for a score of 224. This z-score tells us how many standard deviations the score is above the mean. Using the empirical rule, we can determine the percentage of students who scored above 224.

Step-by-step explanation:

To solve this problem, we can use the empirical rule, also known as the 68-95-99.7 rule, which states that approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations. Since the mean is 200 and the standard deviation is 12, we can calculate the z-score for a score of 224 using the formula:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z = (224 - 200) / 12 ≈ 2

The z-score of 2 tells us that the score of 224 is 2 standard deviations above the mean. Using the empirical rule, we know that approximately 95% of the data falls within 2 standard deviations, so the percentage of students who scored above 224 is approximately 100% - 95% = 5%.