The combined SAT scores for the students at a local high school are normally distributed with a mean of 1520 and a standard deviation of 290 . The local college includes a minimum score of 708 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X>708)= 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. Question Help: ⿴ Message instructor

To find the percentage of students who satisfy the admission requirement based on their SAT scores, we calculate the z-score for the minimum score and find the area under the normal distribution curve to the right of the z-score. The percentage of students who meet the requirement is approximately 99.78%.

Explanation:

To find the percentage of students whose SAT scores satisfy the admission requirement, we need to calculate the z-score for the minimum score of 708 and then find the area under the normal distribution curve to the right of this z-score. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Using the formula, we find the z-score to be (708 - 1520) / 290 = -2.8276. We want to find P(X > 708), which is equivalent to finding P(Z > -2.8276). Using a standard normal distribution table or a calculator, we find that the area to the right of -2.8276 is approximately 0.9978.

So, approximately 99.78% of students from this school earn scores that satisfy the admission requirement.

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