Answer :
Final answer:
The SAT and ACT are crucial in college admissions, with SAT scores being analyzed through z-scores to understand how a student's result compares to the mean. Percentiles are used by colleges to determine admission criteria.
Explanation:
The Scholastic Aptitude Test (SAT) and the American College Testing (ACT) are standardized tests commonly used for college admissions in the United States. Comprehending SAT scores and their implications for college admission is essential for high school students navigating the application process.
Calculating a Z-Score
To calculate a z-score for an SAT score, the following formula is used: z = (x - \\\mu\\) / o, where x is the score, \\\mu\\ is the mean, and o is the standard deviation. If a student scored 720 on the math section of the SAT when the mean is 520 and the standard deviation is 115, the z-score would be (720 - 520) / 115 \\\approx\\ 1.74. This z-score tells us the score is 1.74 standard deviations above the mean.
Percentiles in Admissions
Universities and colleges often use percentiles to compare scores and set admission criteria. For instance, if a college admits students with SAT scores at the 75th percentile, only students who scored as well as or better than this percentile are admitted.
Answer:
10.56% of high school seniors can get into College A
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 500, \sigma = 80[/tex]
What percentage of high school seniors can get into College A
College A accepts people whose scores are above 600, so this is 1 subtracted by the pvalue of Z when X = 600. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{600 - 500}{80}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
10.56% of high school seniors can get into College A
