Answer :
Using z-score, approximately 8.82% of students who took the SAT math test meet the University of Michigan's recommended score of at least 730.
What percent of students who took the SAT math test meet this requirement?
To find out what percent of students who took the SAT math test meet the University of Michigan's recommended score of at least 730, we can use the z-score formula for a normal distribution:
[tex]\[z = \frac{X - \mu}{\sigma}\][/tex]
Where:
- X is the value we want to find the percentile for (in this case, 730).
- μ (mu) is the mean of the distribution (528).
- σ (sigma) is the standard deviation (117).
Now, we can calculate the z-score:
[tex]\[z = \frac{730 - 528}{117} \approx 1.74\][/tex]
Next, we can use a standard normal distribution table or calculator to find the percentile (or percentage) associated with a z-score of 1.74. This will give us the percentage of students who scored below 730.
Using a standard normal distribution table or calculator, you would find that the percentage of students who scored below 730 is approximately 91.18%.
To find the percentage of students who meet or exceed the recommended score of 730, you can subtract this percentage from 100%:
Percentage meeting the requirement = 100% - 91.18% ≈ 8.82%
So, approximately 8.82% of students who took the SAT math test meet the University of Michigan's recommended score of at least 730.
Learn more on z-score here;
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