We appreciate your visit to Standardized tests In a particular year the mean score on the ACT test was 17 5 and the standard deviation was 4 8 The mean. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find Emma's SAT score given her z-score, we can use the z-score formula:
[tex]\text{z-score} = \frac{(X - \mu)}{\sigma}[/tex]
where:
- [tex]X[/tex] is the SAT score we are solving for,
- [tex]\mu[/tex] is the mean SAT score, which is 549,
- [tex]\sigma[/tex] is the standard deviation of SAT scores, which is 120,
- [tex]\text{z-score}[/tex] is given as -2.1.
Rearrange the formula to solve for [tex]X[/tex]:
[tex]X = \mu + (\text{z-score} \times \sigma)[/tex]
Substitute the provided values into the equation:
[tex]X = 549 + (-2.1 \times 120)[/tex]
First, calculate the product:
[tex]-2.1 \times 120 = -252[/tex]
Then, substitute back to find [tex]X[/tex]:
[tex]X = 549 - 252 = 297[/tex]
Thus, Emma's SAT score was 297. This calculation shows how z-scores can be used to determine individual data points from a normal distribution, using the mean and standard deviation.
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