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 843 and a standard deviation of 148. The local college requires a minimum SAT score of 863 before students are considered for admission.

What percentage of students from this school have SAT scores that do not satisfy the local college's admission requirement? Enter your answer as a percent accurate to 2 decimal places.

Answer :

Approximately 45.17% of students from this school have SAT scores that do not satisfy the local college's admission requirement.

To calculate the percentage of students with SAT scores that do not satisfy the local college's admission requirement, we need to find the probability that a randomly selected student from the school has an SAT score less than 863.

Using the properties of the standard normal distribution, we find the z-score for 863 using the formula:

z = (X - μ) / σ

where X is the required minimum SAT score (863), μ is the mean SAT score (843), and σ is the standard deviation (148). Substituting the values:

z = (863 - 843) / 148 ≈ 0.1351

Using the standard normal distribution table or a statistical calculator, we find that P(Z < 0.1351) ≈ 0.5483.

Since the standard normal distribution is symmetrical around the mean, we can find the percentage of students with scores less than 863 by subtracting the probability from 0.5 (which represents the area to the right of the mean). Therefore, the percentage of students with scores less than 863 is approximately 0.5 - 0.5483 = 0.4517.

To express this as a percentage, we multiply by 100:

0.4517 * 100 ≈ 45.17%

So, approximately 45.17% of students from this school have SAT scores that do not satisfy the local college's admission requirement.

You can learn more about SAT scores at

https://brainly.com/question/3121844

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