The combined SAT scores for the students at a local high school are normally distributed with a mean of 1548 and a standard deviation of 299. The local college requires a minimum score of 2266 for admission.

What percentage of students from this school earn scores that fail to satisfy the admission requirement?

[tex]P(X < 2266) = \%[/tex]

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

Within the realm of statistics, one calculates the percentage of students falling below a given SAT score by determining the z-score, which in turn is used to find a percentile in the standard normal distribution. Exact calculations were not performed due to lack of specific data.

Explanation:

The question relates to the field of statistics within mathematics, specifically the area that deals with normal distribution and the calculation of percentiles using the mean and standard deviation of SAT scores. When a local high school has an average SAT score of 1548 with a standard deviation of 299, and the local college requires a minimum SAT score of 2266 for admission, we need to calculate the percentage of students whose SAT scores fall below the 2266 threshold.

To find this, a z-score needs to be calculated followed by a lookup in the standard normal (z) distribution table, or the use of a statistical calculator or software. Unfortunately, specific calculations are not provided in this instance. However, typically one would subtract the mean from the score in question and divide the result by the standard deviation. The z-score indicates how many standard deviations the desired value (2266) is from the mean (1548), and this score can then be converted to a percentile which represents the percentage of students scoring below the admission requirement.