The combined SAT scores for the students at a local high school are normally distributed with a mean of 1463 and a standard deviation of 304. The local college includes a minimum score of 1250 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement?

Calculate \( P(X > 1250) \).

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

Question

15-09-2023
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 1463 and a standard deviation of 304. The local college includes a minimum score of 1250 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement?

Calculate \( P(X > 1250) \).

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

Answer :

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afreenmajid123 afreenmajid123 · Answer 1 · 2025-03-30T07:50:08-04:00

Final answer:

To find the percentage of students from the school that earn scores satisfying the admission requirement, we need to calculate the probability that a student's SAT score is greater than 1250.

Explanation:

To find the percentage of students from the school that earn scores satisfying the admission requirement, we need to calculate the probability that a student's SAT score is greater than 1250. We can use the z-score formula to convert the given minimum score to a z-score and then use the standard normal table to find the percentage.

First, calculate the z-score using the formula: z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. Plugging in the values, we get z = (1250 - 1463) / 304 = -0.4375.

Next, use the standard normal table or a calculator to find the percentage corresponding to the z-score. From the table, we find that the area to the left of -0.4375 is approximately 0.3311. However, we want to find the area to the right of 1250, so we subtract this from 1 to get 0.6689.

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