The combined SAT scores for the students at a local high school are normally distributed with a mean of 1479 and a standard deviation of 310. The local college includes a minimum score of 642 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? P(X < 642) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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**Understanding SAT Score Distribution and Admission Requirements**

The combined SAT scores for the students at a local high school follow a normal distribution with a mean (average) score of 1479 and a standard deviation of 310. The local college has set a minimum SAT score requirement of 642 for admission.

**Question:**

What percentage of students from this school score below the required admission score?

\[ P(X < 642) = \_\_ \% \]

*Instructions:* 

- Enter your calculation as a percentage accurate to one decimal place (omit the "%" symbol).
- You may use exact z-scores or z-scores rounded to three decimal places to obtain your answer.
Transcribed Image Text:**Understanding SAT Score Distribution and Admission Requirements** The combined SAT scores for the students at a local high school follow a normal distribution with a mean (average) score of 1479 and a standard deviation of 310. The local college has set a minimum SAT score requirement of 642 for admission. **Question:** What percentage of students from this school score below the required admission score? \[ P(X < 642) = \_\_ \% \] *Instructions:* - Enter your calculation as a percentage accurate to one decimal place (omit the "%" symbol). - You may use exact z-scores or z-scores rounded to three decimal places to obtain your answer.
Expert Solution
Step 1

Given:

Mean μ = 1479

Standard deviation σ = 310

X = 642

Formula Used:

Z-score = X-μσ

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