The combined SAT scores for the students at a local high school are normally distributed with a mean of 1488 and a standard deviation of 298. The local college includes a minimum score of 2382 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement?

Calculate $ P(x < 2382) $.

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.

By calculating the Z-score (which measures how many standard deviations an element is from the mean) for the admission score, we determine that less than 0.5% of the students fail to meet the admission requirement due to the admission score being three standard deviations from the mean of the SAT scores.

Explanation:

To calculate the percentage of students that do not meet the admission requirements, we first need to calculate the Z-score for the minimum admission score. The Z-score provides a measure of how many standard deviations an element is from the mean. In this context, it shows how many standard deviations the minimum admission score is from the average SAT score.

The Z-score is determined using the following formula:

Z = (X - μ) / σ

where:
Z = Z-score
X = value
μ = mean
σ = standard deviation

Substituting the given values, the Z-score will calculated as follows:

Z = (2382 - 1488) / 298 = 2.999 ~ 3

A Z-score of 3 indicates the value is 3 standard deviations to the right of the mean. To find the percentage of students that didn't meet the requirement, we look for the Z-score in the Z-table or use a calculator, which tells the area to the left of Z

Therefore, the percentage of students who failed to meet the admissions requirement = (1 - Z-table value or calculator result) * 100.

For a Z-score of 3, this value is close to 100% (exactly 99.87%), so only a very small proportion of students (less than 0.5%) do not meet the admission requirement.

Learn more about statistics here:

https://brainly.com/question/31538429

#SPJ11