Respuesta :
To be in the top 10% of the population, a student must have a minimum SAT score of 628.
What is the standard deviation?
- The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
- While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
- The square root of the variance is used to determine the standard deviation.
- An alternative method of calculating it is to identify the mean of a data set, compare each data point to the mean, square the differences, add them all up, divide by the number of points in the data set minus 1, and then calculate the square root.
So, the minimum SAT score needed to be in the highest 10% of the population:
This is the 90th percentile, which is X when Z has a p-value of 0.9, or X when Z = 1.28. It is calculated as 100 - 10 = X.
[tex]\begin{aligned}&Z=\frac{X-\mu}{\sigma} \\&1.28=\frac{X-500}{100} \\&X-500=1.28(100) \\&X=628\end{aligned}[/tex]
To be in the top 10% of the population, a score of 628 on the SAT is required.
Therefore, to be in the top 10% of the population, a student must have a minimum SAT score of 628.
Know more about the standard deviation here:
https://brainly.com/question/475676
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The correct question:
The distribution of scores on the SAT is approximately normal with a mean of mu = 500 and a standard deviation of sigma = 100. For the population of students who have taken the SAT.
What is the minimum SAT score needed to be in the highest 10% of the population?
