The combined SAT scores for the students at a local high school are normally distributed with a mean of 1480 and a standard deviation of 299. The local college includes a minimum score of 1540 in its admission requirements.

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

\[ P(X < 1540) = \, \% \]

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

To calculate the percentage of students who fail to satisfy the admission requirement, we need to calculate the area under the normal distribution curve to the left of the score 1540.

Explanation:

To find the percentage of students who earn scores that fail to satisfy the admission requirement, we need to calculate the area under the normal distribution curve to the left of the score 1540. This can be done by calculating the z-score and then using a z-table or a calculator that provides the area under the normal curve.

The z-score can be calculated using the formula: z = (X - mean) / standard deviation Substituting the given values, we have: z = (1540 - 1480) / 299 = 0.2 Using a z-table or a calculator, we can find that the area to the left of the z-score 0.2 is approximately 0.5793. Therefore, approximately 57.9% of students from this school earn scores that fail to satisfy the admission requirement.

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