Answer :
The percentage of the class that scored below 400 is approximately 16%.
The given SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. We need to find the percentage of the class that scored below 400.
To solve this problem, we can use the z-score formula.
z = (x - μ)/σ
Where x is the score, μ is the mean, and σ is the standard deviation.
We can rearrange this formula to find x as follows:
x = zσ + μ
Now we can find the z-score for a score of 400 as follows:
z = (400 - 500)/100
= -1
Plug this value of z into the equation above to find the corresponding score:
x = (-1)(100) + 500
= 400
So a score of 400 has a z-score of -1. This means that approximately 16% of the class scored below 400. This can be determined using the 68-95-99.7 rule.
The 68-95-99.7 rule states that:
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
A z-score of -1 falls within one standard deviation of the mean, which means that approximately 68% of the data falls above this score.
Therefore, the correct answer is 16%.
To learn more about the z-score formula from the given link.
https://brainly.com/question/25638875
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