To find: To determine the statements that are not true.
A.I and II are NOT true.
Given information:
Given,a set of data is
Given statements are:
- 68% of the values are between 37.6 and 50.4
- 13.5% of the values are less than 40.8
- 5% of the values are lower than 37.6 or higher than 50.4
Calculation:
One standard deviation below and above the mean are:
Two standard deviation below and above the mean are:
In a normal distribution, the data is distributed equally i.e., 50% on either side of the mean.
The data within the first standard deviation contains 34% of data on each side.
The data between the first standard deviation and second standard deviation contains 13.5% of data on each side.
The data between the second standard deviation and third standard deviation contains 2.35% of data on each side.
Here, 37.6 and 50.4are the second standard deviationson either sides of themean.
Hence the percent of data between 37.6 and 50.4is given by:
Hence the statement I is NOT true.
Also, 40.8 is the first standard deviation on the left of the mean. The data to the right of this is
So the data percent of values less than 40.8 is
Hence the statement II is NOT true.
The percent of data between 37.6 and 50.4 is 95%. Hence the percent of data lower than 37.6 and higher than 50.4 is
Hence the statement III is true.
Conclusion:
A.I and II are NOT true.
Chapter 12 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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