High School

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 847 and a standard deviation of 141. The local college requires a minimum SAT score of 864 for admission. What percentage of students from this school have SAT scores that do not satisfy the local college's admission requirement?

Answer :

Around 45.15% of students have SAT scores below 864, not meeting the college's admission requirement.

To find the percentage of students from this school who have SAT scores that do not satisfy the local college's admission requirement (which is an SAT score of at least 864), we can use the standard normal distribution (Z-distribution).

First, we need to standardize the minimum required score using the given mean (μ=847μ=847) and standard deviation (σ=141σ=141):

Z=X−μσ=864−847141Z=σX−μ​=141864−847​

Calculate the value of Z:

Z=17141≈0.1206Z=14117​≈0.1206

Now, we want to find the percentage of students with SAT scores below 864, which is the area to the left of ZZ in the standard normal distribution.

Using a standard normal distribution table or calculator, we can find that the cumulative probability for Z=0.1206Z=0.1206 is approximately 0.5485.

However, since we are interested in the percentage of students with scores below 864, we need to subtract this probability from 1 to get the percentage of students with scores that do not satisfy the admission requirement:

Percentage=1−0.5485≈0.4515Percentage=1−0.5485≈0.4515

Multiply this by 100 to convert to a percentage:

Percentage≈45.15%Percentage≈45.15%

So, approximately 45.15% of students from this school have SAT scores that do not satisfy the local college's admission requirement.

To know more about probability visit:

https://brainly.com/question/23417919

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