We appreciate your visit to In the class of 2019 more than 1 6 million students took the SAT The distribution of scores on the math section out of 800. 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 :
Answer:
32 . 6 %
Step-by-step explanation:
500 IS 28 BELOW THE MEAN and z-score = 28/117 = - .239
600 is 72 ABOVE the mean and z-score = 72/117 = .615
Look up these z-scores in the table to find z =- .239 =.4052
z = .615 =.7308
.7308 - .4052 = 32.6 %
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Final answer:
The proportion of students who scored between 500 and 600 on the SAT math test is approximately 32.72%, which was calculated using Z-scores and the area under the normal distribution curve.
Explanation:
To find the proportion of students who scored between 500 and 600 on the SAT math test, we will need to calculate the Z-scores for both 500 and 600 and then find the area under the normal curve between these two values. The formula for a Z-score is Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
The Z-score for 500 is Z1 = (500 - 528) / 117 = -0.24 and for 600 is Z2 = (600 - 528) / 117 = 0.62. Now, using the normal distribution table, we determine the proportion of students who obtained scores below 600 and below 500. The values corresponding to Z1 and Z2 are approximately 0.4052 and 0.7324 respectively.
Finally, to find the proportion of students who scored between 500 and 600, we subtract the proportion of students who scored below 500 from the proportion who scored below 600. So the proportion of students who scored between 500 and 600 is 0.7324 - 0.4052 = 0.3272 or approximately 32.72%.
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