Normal Distribution Test Scores: Percentages & Interpretation for a School

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Scores on a standardized test at a school are normally distributed with a mean of 720 and a standard deviation of 83. To find the percentage of students scoring less than 650, one must calculate the z-score and use the standard normal distribution table. For scores between 500 and 780, the z-scores for both values should be determined to find the corresponding percentages. A student in the 97th percentile scored higher than approximately 97% of their peers, indicating a score around 860 or higher. Understanding these calculations is essential for interpreting test score distributions effectively.
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2. Suppose that scores on a standardized test in a school are normally distributed with a mean 720 and standard deviation 83.
a. find the percentage of students scoring less than 650
b. find the percentage scoring between 500 and 780
c. if you were told that a student scored in 97th percentile, what could you say about that students score?

thanks in advance
 
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