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Answer :
Approximately 0.4% of students from the school earn scores that fail to satisfy the admission requirement. This means that a very small percentage of students have SAT scores below 957, which may impact their eligibility for admission to the local college.
To find the percentage of students from the school who earn scores that fail to satisfy the admission requirement, we need to calculate the probability that a student's SAT score is less than 957.
We can convert the SAT scores to Z-scores using the formula:
Z = (X - μ) / σ
where X is the individual SAT score, μ is the mean (1538), and σ is the standard deviation (306).
Substituting the values, we have:
Z = (957 - 1538) / 306 ≈ -2.65
Using the standard normal distribution table or a statistical calculator, we can find the probability associated with a Z-score of -2.65, which represents the percentage of students whose scores fall below 957.
The percentage of students who earn scores that fail to satisfy the admission requirement is approximately 0.4% (or 0.004 when expressed as a decimal).
The given problem involves a normal distribution of combined SAT scores for students at a local high school. We are given the mean (μ) of 1538 and the standard deviation (σ) of 306.
To determine the percentage of students who fail to satisfy the admission requirement, we need to calculate the probability that a student's SAT score is below 957, which is the admission requirement. This is equivalent to finding the probability of X < 957, where X represents the SAT scores.
To calculate this probability, we convert the SAT score of 957 to a Z-score using the formula Z = (X - μ) / σ. By substituting the values, we obtain a Z-score of approximately -2.65.
The Z-score represents the number of standard deviations that a particular value is from the mean. Using the standard normal distribution table or a statistical calculator, we can find the probability associated with a Z-score of -2.65, which is approximately 0.004.
Therefore, approximately 0.4% of students from the school earn scores that fail to satisfy the admission requirement. This means that a very small percentage of students have SAT scores below 957, which may impact their eligibility for admission to the local college.
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