The distribution of student scores on the quantitative section of the SATs has an approximately normal distribution with a mean score of 501 points and a standard deviation of 85 points. Suppose a college with competitive admissions will only accept students who scored at least 550 on the quantitative section of the SATs. What proportion of students will NOT qualify for acceptance at that college based on SAT scores? Provide four decimal places in your answer.

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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