To find: The whole number of standard deviations from the mean that include all the data values given.
The data falls within 3 standard deviations of the mean.
Given information:
The mean length of Beethoven’s nine symphonies is 37 minutes; the standard deviation is 12 minutes.
The given data set is 27 min, 30 min, 47 min, 35 min, 30 min, 40 min, 35 min, 22 min, 65 min.
Calculation:
The minimum and maximum values of the data are 22 min and 65 min respectively.
1 standard deviation below the mean:
2 standard deviations below the mean:
Hence the minimum value falls within two standard deviations of the mean.
1 standard deviation above the mean:
2 standard deviations above the mean:
3 standard deviations above the mean:
Hence the maximum value falls within three standard deviations of the mean.
Conclusion:
The data falls within 3 standard deviations of the mean.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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