Answer :
The 4.45% of the students at this high school fail to meet the college's admission requirement of a minimum SAT score of 2054. This implies that the score of 2054 is approximately 1.7 standard deviations above the mean score.
The z-score associated with the cut-off score of 2054. The z-score is a measure that tells us how far a particular data point is from the mean in terms of standard deviations. It is calculated using the formula:
z = (X - μ) / σ
Where X is the data point, μ represents the mean, and σ represents the standard deviation. Substituting the given values into the formula gives:
z = (2054 - 1549) / 297 = 1.70
This implies that the score of 2054 is approximately 1.7 standard deviations above the mean score.
Next, we can use the calculated z-score to determine the percentage of students who met or exceeded the cut-off score, which is equal to the cumulative distribution function (CDF) evaluated at the z-score. For our z-score of 1.7, this gives a CDF value of 95.55%.
Finally, to answer the question, we need to find the complement of this percentage, which represents the percentage of students who fail to meet the admission requirement. We can calculate this by subtracting the obtained percentage from 100%, which yields:
Failure percentage = 100% - 95.55% = 4.45%
Therefore, approximately 4.45% of the students at this high school fail to meet the college's admission requirement of a minimum SAT score of 2054.
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