Score: $5 / 9 \quad 5 / 9$ answered
Question 6
The combined SAT scores for the students at a local high school are normally distributed with a mean of 1538 and a standard deviation of 298 . The local college includes a minimum score of 1240 in its admission requirements.
What percentage of students from this school earn scores that fail to satisfy the admission requirement?
\[
P(X< 1240)=
\]
\%
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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Answer
\(\boxed{15.9\%}\) is the final answer
Step 1 ：Calculate the z-score using the formula \(Z = \frac{X - \mu}{\sigma}\)
Step 2 ：Substitute the given values into the formula to get \(Z = \frac{1240 - 1538}{298} = -1\)
Step 3 ：The z-score of -1 means that a score of 1240 is one standard deviation below the mean
Step 4 ：Look up a z-score of -1 in the z-table to find the percentage of students who score below this
Step 5 ：Approximately 15.9% of students from this school earn scores that fail to satisfy the admission requirement
Step 6 ：\(\boxed{15.9\%}\) is the final answer
