The combined SAT scores for the students at a local high school are normally distributed with a mean of 1487 and a standard deviation of 306. The local college requires a minimum score of 2344 for admission. What percentage of students from this school earn scores that fail to satisfy the admission requirements?

Question

04-06-2025
Mathematics

High School

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1487 and a standard deviation of 306. The local college requires a minimum score of 2344 for admission. What percentage of students from this school earn scores that fail to satisfy the admission requirements?

Answer :

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niludas niludas · Answer 1 · 2023-09-13T12:37:08-04:00

Final answer:

To calculate the percentage of students from this school who fail to satisfy the admission requirement, we need to find the percentage of students with SAT scores below 2344. Using the normal distribution and the z-table, we can calculate the z-score for a score of 2344 and find the corresponding percentage.

Explanation:

To calculate the percentage of students from this school who earn scores that fail to satisfy the admission requirement, we need to find the percentage of students whose SAT scores are below 2344.

To do this, we can use the normal distribution and standard normal table (also known as the z-table). We first need to convert the SAT score of 2344 to a z-score, which measures the number of standard deviations a data point is from the mean.

Using the formula z = (x - mean) / standard deviation and plugging in the values mean = 1487, standard deviation = 306, and x = 2344, we can calculate the z-score as z = (2344 - 1487) / 306 ≈ 2.81.

Next, we can look up the percentage of students below a z-score of 2.81 in the standard normal table. From the table, we can find that approximately 99.6% of the students have scores below 2344. Therefore, the percentage of students from this school who earn scores that fail to satisfy the admission requirement is approximately 100% - 99.6% = 0.4%.