To explain: Whether Jake and Elena scored top 10% of their group in a standardized test.
Jake score is not in the top 10% of his group but Elena scored in the top 10% of her group.
Given:
The score of Jake and Elena in a standardized test in different classes
The mean and standard deviation of Jake’s group
The mean and standard deviation of Elena’s group
Concept used:
The probabilities of data less than a particular score in a
Calculation:
The Z score for Jake’s test score is calculated as shown below
The Z score for Jake’s test score with respect to the mean and standard deviation of his group is 1.17 (rounded to two decimal places).
The Z score for Elena’s test score is calculated as shown below
The Z score for Elena’s test score with respect to the mean and standard deviation of her group is 2.75 (rounded to two decimal places).
With respect to the Z table the probability less than Z score 1.17 is
The probability less than Z score 2.75 is
Interpretation:
The percentage of students who scores less than Jake in his group is 87.9%. The percentage of students who scores less than Elena in her group is 99.7%. Thus Jake is not in the top 10% of students in his group whereas Elena is in the top 10% of students in her group.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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