We appreciate your visit to When you apply to college you either submit an SAT score or an ACT score for admission Your friend scored a 30 on the ACT. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The z-score for a friend's ACT score of 30 is 1.91, which corresponds to the 97.2nd percentile in a normal distribution, indicating that about 2.8% of students scored higher than the friend.
Explanation:
To determine the percentage of students who scored higher than your friend on the ACT, we need to calculate the z-score for your friend's ACT score and then use the standard normal distribution to find the corresponding percentile.
The z-score is calculated using the formula: z = (X - µ) / σ, where X is the score of interest, µ is the mean, and σ is the standard deviation. For your friend's score, the z-score would be (30 - 21) / 4.7 = 1.91.
Consulting a standard normal distribution table or using a calculator with statistical functions, we find that a z-score of 1.91 corresponds to a percentile of approximately 97.2%. This means that your friend scored better than approximately 97.2% of test-takers, and therefore, only about 2.8% scored higher than your friend.
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