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Answer :
Final answer:
The proportion of students who will NOT qualify for acceptance at the college based on SAT scores is approximately 0.2810.
Explanation:
To find the proportion of students who will NOT qualify for acceptance at the college based on SAT scores, we need to calculate the z-score for a score of 550. The formula for z-score is: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. Substituting the values, we get z = (550 - 501) / 85 = 0.5765. We can then use a standard normal distribution table or calculator to find the proportion of students with a z-score less than 0.5765, which is approximately 0.7190. Therefore, the proportion of students who will NOT qualify for acceptance at the college based on SAT scores is 1 - 0.7190 = 0.2810.
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