Answer :
To determine where about 68% of the data lies, we can use the concept of standard deviation. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
Here's how you can calculate that:
1. Understand the Mean and Standard Deviation:
- The mean (average) of the data set is 131.
- The standard deviation, which measures how much the data varies from the mean, is 8.
2. Calculate the Range for 68% of the Data:
- Since 68% of the data falls within one standard deviation of the mean, we will calculate this range.
- Subtract the standard deviation from the mean to find the lower bound:
- Lower bound = Mean - Standard Deviation = 131 - 8 = 123
- Add the standard deviation to the mean to find the upper bound:
- Upper bound = Mean + Standard Deviation = 131 + 8 = 139
3. Result:
- About 68% of the data will lie between 123 and 139.
Therefore, the correct range where about 68% of the data lies is from 123 to 139.
Here's how you can calculate that:
1. Understand the Mean and Standard Deviation:
- The mean (average) of the data set is 131.
- The standard deviation, which measures how much the data varies from the mean, is 8.
2. Calculate the Range for 68% of the Data:
- Since 68% of the data falls within one standard deviation of the mean, we will calculate this range.
- Subtract the standard deviation from the mean to find the lower bound:
- Lower bound = Mean - Standard Deviation = 131 - 8 = 123
- Add the standard deviation to the mean to find the upper bound:
- Upper bound = Mean + Standard Deviation = 131 + 8 = 139
3. Result:
- About 68% of the data will lie between 123 and 139.
Therefore, the correct range where about 68% of the data lies is from 123 to 139.
