The combined SAT scores for the students at a local high school are normally distributed with a mean of 879 and a standard deviation of 163. The local college requires a minimum SAT score of 873 before students are considered for admission.

What percentage of students from this school have SAT scores that do not satisfy the local college's admission requirement?

Enter your answer as a percent accurate to 2 decimal places. %

To determine the percentage of students from the high school whose SAT scores do not satisfy the local college's admission requirement, we need to calculate the probability that a randomly selected student has a score below 873.

Since the SAT scores are normally distributed with a mean of 879 and a standard deviation of 163, we can use the z-score formula to standardize the value of 873:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

Plugging in the values:

z = (873 - 879) / 163 = -0.0368

Looking up the z-score of -0.0368 in the standard normal distribution table or using a calculator, we find that the area to the left of this z-score is approximately 0.4861.

To find the percentage of students whose SAT scores do not satisfy the admission requirement, we subtract this probability from 1 (since we want the area to the right of the z-score):

percentage = (1 - 0.4861) * 100 = 51.39%

Therefore, approximately 51.39%(percent) of students from this high school have SAT scores that do not satisfy the local college's admission requirement.

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