High School

Use the 68-95-99.7 rule. Assume that math SAT scores in a class are normally distributed with a mean of 500 and a standard deviation of 100. What percentage of the class scored below 400?

A. 66%
B. 34%
C. 84%
D. 16%

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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