Answer :
Final answer:
In order to place in the top 8% of all students, Abigail needs to score around 1291 on the SAT. This result has been calculated using the Z-score formula.
Explanation:
The question is asking for the SAT score that Abigail needs to be in the top 8% of all students. In statistical terms, this is the 80th percentile of the SAT scores. We can calculate this using the z-score formula: Z = (X - μ) / σ. The Z-score represents how many standard deviations an element is from the mean.
From the given data, the SAT has a mean (μ) of 1026 and a standard deviation (σ) of 209. A Z-score for the 80th percentile is approximately 1.285 (based on the normal distribution table). Placing this into the formula, we have 1.285 = (X - 1026) / 209.
Solving for X, we get X = (1.285 * 209) + 1026 = 1291. Therefore, Abigail needs to score around 1291 on the SAT to be in the top 8% of all students.
Learn more about SAT score calculation here:
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Answer:
1321.
Step-by-step explanation:
We have been given that SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean μ = 1026 and standard deviation σ = 209. We are asked to find the score that Abigail must get on the SAT in order to place in the top 8% of all students.
Top 8% is equal to 92% or more.
Let us find z-score corresponding to 92% or 0.92. Using normal distribution table, we get a z-score equal to 1.41.
Now, we will z-score formula to solve for the score as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]1.41=\frac{x-1026}{209}[/tex]
[tex]1.41*209=\frac{x-1026}{209}*209[/tex]
[tex]294.69=x-1026[/tex]
[tex]294.69+1026=x-1026+1026[/tex]
[tex]1320.69=x[/tex]
[tex]x\approx 1321[/tex]
Therefore, Abigail must get a score of 1321 on the SAT in order to place in the top 8% of all students.
