SOLUTION: The national average for math portion of the college board's SAT is 521 with a standard deviation of 84. The median is 521. What is the shape of the SAT math score distribution? Wh
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Question 986673: The national average for math portion of the college board's SAT is 521 with a standard deviation of 84. The median is 521. What is the shape of the SAT math score distribution? Why? and What rule (empirical or Chebyshev's) predicts that how many percent of the SAT math score data should lie between a 353 and 689, which are +/-(number) standard deviation away from the mean
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Q: What is the shape of the SAT math score distribution?
A: The distribution is most likely normal. In other words a standard bell curve like shown below
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Q: Why?
A: The majority of the distribution is clustered at or around the mean/median. The center of the distribution is where the most values are located. If we say "the average male is 6', then we expect the heights to be close to 6 feet or clustered around there. The same applies to the test scores. The more values in the center, the higher the peak. The more extreme values are less likely which explains why there is a drop off: there are less values out in those regions. The further away from the mean, the less likely you'll pick a value from it. All of this contributes to the overall bell shaped curve.
Note: the x axis is the test score while the y axis is the frequency
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Q: What rule (empirical or Chebyshev's) predicts that how many percent of the SAT math score data should lie between a 353 and 689, which are +/-(number) standard deviation away from the mean
A: Notice how 521-2*84 = 353 and 521+2*84 = 689. This suggests that the 353 is 2 std deviations below the mean. Also, 689 is 2 std deviations above the mean. You'll use the empirical rule to get roughly 95% of the distribution is between those two values. So if 100 people took the test, we'd expect about 95 of them to score between 353 and 689
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